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heegner_index() output

asked 8 years ago

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

This elliptic curve has rank 1 over Q. I am interested in knowing which primes divide the index of the Heegner point yK in the group E(K) modulo torsion where K=Q(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 8 years ago

FrédéricC gravatar image

The answer is an interval:

sage: E = EllipticCurve('37a')
sage: idx = E.heegner_index(-7); idx
1.00000?
sage: idx.parent()
Real Interval Field with 20 bits of precision
sage: idx.lower()
0.99999
sage: idx.upper()
1.0001
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Asked: 8 years ago

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Last updated: Oct 12 '16