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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 277725a
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 277725.a1 | 277725a1 | \([0, -1, 1, -162068158, -1041095638032]\) | \(-2476357085090396229632/1030161895751953125\) | \(-195843434150218963623046875\) | \([]\) | \(165224448\) | \(3.7530\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 277725a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 277725a do not have complex multiplication.Modular form 277725.2.a.a
sage: E.q_eigenform(10)