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SageMath
sage: E = EllipticCurve("p1")
sage: E.isogeny_class()
Elliptic curves in class 221067.p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 221067.p1 | 221067o1 | \([0, 0, 1, -165198, -25170093]\) | \(5652299539972096/168301718109\) | \(14845726252676781\) | \([]\) | \(1128960\) | \(1.8799\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 221067.p1 has rank \(2\).
Complex multiplication
The elliptic curves in class 221067.p do not have complex multiplication.Modular form 221067.2.a.p
sage: E.q_eigenform(10)