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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 7840.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7840.b1 | 7840o1 | \([0, 0, 0, 1465688, -670046384]\) | \(722603599520256/820654296875\) | \(-395465348600000000000\) | \([]\) | \(506880\) | \(2.6386\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7840.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 7840.b do not have complex multiplication.Modular form 7840.2.a.b
sage: E.q_eigenform(10)