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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 277725j
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277725.j1 | 277725j1 | \([0, -1, 1, -85734055758, 12667696500377918]\) | \(-2476357085090396229632/1030161895751953125\) | \(-28991856879240623824596405029296875\) | \([]\) | \(3800162304\) | \(5.3208\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 277725j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 277725j do not have complex multiplication.Modular form 277725.2.a.j
sage: E.q_eigenform(10)