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SageMath
E = EllipticCurve("cp1")
E.isogeny_class()
Elliptic curves in class 121968cp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 121968.dq1 | 121968cp1 | \([0, 0, 0, -4752, 90288]\) | \(1216512/343\) | \(3346036936704\) | \([]\) | \(138240\) | \(1.1102\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 121968cp1 has rank \(1\).
Complex multiplication
The elliptic curves in class 121968cp do not have complex multiplication.Modular form 121968.2.a.cp
sage: E.q_eigenform(10)