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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 21175b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21175.bc1 | 21175b1 | \([1, 1, 0, -35, 70]\) | \(-148955/7\) | \(-232925\) | \([]\) | \(2304\) | \(-0.20713\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21175b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21175b do not have complex multiplication.Modular form 21175.2.a.b
sage: E.q_eigenform(10)