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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 12635f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 12635.d1 | 12635f1 | \([1, 0, 0, -910, -13643]\) | \(-1771561/665\) | \(-31285510865\) | \([]\) | \(8640\) | \(0.72377\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12635f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 12635f do not have complex multiplication.Modular form 12635.2.a.f
sage: E.q_eigenform(10)