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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 10008c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 10008.d1 | 10008c1 | \([0, 0, 0, 117, 54]\) | \(237276/139\) | \(-103762944\) | \([]\) | \(2048\) | \(0.22754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10008c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10008c do not have complex multiplication.Modular form 10008.2.a.c
sage: E.q_eigenform(10)