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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 7740b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7740.a1 | 7740b1 | \([0, 0, 0, -41808, -3301868]\) | \(-43304636317696/176326875\) | \(-32906826720000\) | \([]\) | \(24576\) | \(1.4499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7740b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 7740b do not have complex multiplication.Modular form 7740.2.a.b
sage: E.q_eigenform(10)