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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 122694c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 122694.t1 | 122694c1 | \([1, 1, 0, -2228437, -1283607827]\) | \(-32193903207227411/66119763456\) | \(-2513522376772932096\) | \([]\) | \(2643840\) | \(2.4170\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 122694c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 122694c do not have complex multiplication.Modular form 122694.2.a.c
sage: E.q_eigenform(10)