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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 111012c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 111012.b1 | 111012c1 | \([0, -1, 0, -239475460925, 45106634095494489]\) | \(-11859948880710132130963456/375913713056211\) | \(-48140668554040367439859397376\) | \([]\) | \(345772800\) | \(5.0066\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 111012c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 111012c do not have complex multiplication.Modular form 111012.2.a.c
sage: E.q_eigenform(10)