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heegner_index() output

asked 2016-10-12 00:23:55 +0200

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Consider the elliptic curve E=EllipticCurve('37a')

This elliptic curve has rank 1 over $\mathbb{Q}$. I am interested in knowing which primes divide the index of the Heegner point $y_K$ in the group $E(K)$ modulo torsion where $K=\mathbb{Q}(\sqrt{-7})$

Since $E$ has rank 1, heegner_index_bound() does not work so I try E.heegner_index(-7). The output is 1.00000?

This output should be an interval. I do not understand the output. What does the question mark mean?

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answered 2016-10-12 18:55:34 +0200

FrédéricC gravatar image

The answer is an interval:

sage: E = EllipticCurve('37a')
sage: idx = E.heegner_index(-7); idx
sage: idx.parent()
Real Interval Field with 20 bits of precision
sage: idx.lower()
sage: idx.upper()
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Asked: 2016-10-12 00:23:55 +0200

Seen: 359 times

Last updated: Oct 12 '16