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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 693b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
693.c1 | 693b1 | \([0, 0, 1, 18, -7]\) | \(884736/539\) | \(-392931\) | \([]\) | \(56\) | \(-0.23735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 693b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 693b do not have complex multiplication.Modular form 693.2.a.b
sage: E.q_eigenform(10)