Finding Cremona label of the elliptic curve $y^2 = x^3 - x^2 - 1008x + 48512$

asked 2016-06-03 08:59:08 +0100

Suman
25 ●2 ●7

I want to find out the Cremona label of the elliptic curve given by $$y^2 = x^3 - x^2 - 1008x + 48512.$$ I have tried the following commands in Sage but getting errors.

1) E=EllipticCurve(QQ,[0, -1, 0, -1008, 48512]);E.cremona_label()

2) d=CremonaDatabase().data_from_coefficients([0, -1, 0, -1008, 48512]) d['cremona_label']

I would like to know why I am getting errors and also how to find out the Cremona label of the above elliptic curve.

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answered 2016-06-03 16:50:03 +0100

B r u n o
1603 ●5 ●21 ●43

You need to install the optional package database_cremona_ellcurve which contains many more curves than the default database included into Sage:

sage -i database_cremona_ellcurve

Then your first try works:

sage: E = EllipticCurve(QQ,[0, -1, 0, -1008, 48512])
sage: E.cremona_label()
'48400ch1'

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I know this is a very old thread. My recent work on EC and MPC has led me here. I am using SageMath 9.2 on Windows and command

sage -i database_cremona_ellcurve

does not work.

The process

make[8]: Entering directory '/opt/sagemath-9.2'
make build/make/Makefile --stop

goes on forever and I have to reboot Windows (at 'make[2xxx]') to get rid of all the 'make' process.

What have I done wrong?

tigger ( 2021-07-01 14:18:30 +0100 )edit

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answered 2016-06-03 13:40:18 +0100

slelievre
17704 ●22 ●160 ●350 http://carva.org/samue...

Try querying the LMFDB (L-functions and modular forms database) http://lmfdb.org

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Finding Cremona label of the elliptic curve $y^2 = x^3 - x^2 - 1008x + 48512$

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Finding Cremona label of the elliptic curve $y^2 = x^3 - x^2 - 1008x + 48512$