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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 1694b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 1694.d1 | 1694b1 | \([1, -1, 0, -1051, 21797]\) | \(-8773917273/8605184\) | \(-125988498944\) | \([]\) | \(4320\) | \(0.82589\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1694b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 1694b do not have complex multiplication.Modular form 1694.2.a.b
sage: E.q_eigenform(10)