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SageMath
E = EllipticCurve("cf1")
E.isogeny_class()
Elliptic curves in class 121968.cf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121968.cf1 | 121968di1 | \([0, 0, 0, 2172192, -2086576756]\) | \(2575826944/5764801\) | \(-2536798546411738608384\) | \([]\) | \(4561920\) | \(2.7912\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121968.cf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121968.cf do not have complex multiplication.Modular form 121968.2.a.cf
sage: E.q_eigenform(10)