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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 112710cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 112710.cs1 | 112710cl1 | \([1, 0, 0, -268691, -53630175]\) | \(-7423100311456129681/239616000\) | \(-69249024000\) | \([]\) | \(604800\) | \(1.5819\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 112710cl1 has rank \(1\).
Complex multiplication
The elliptic curves in class 112710cl do not have complex multiplication.Modular form 112710.2.a.cl
sage: E.q_eigenform(10)