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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 128576c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 128576.cl1 | 128576c1 | \([0, 1, 0, -2025, 34271]\) | \(373698304/1681\) | \(4132946944\) | \([]\) | \(78336\) | \(0.69682\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 128576c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 128576c do not have complex multiplication.Modular form 128576.2.a.c
sage: E.q_eigenform(10)