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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 301530p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 301530.p1 | 301530p1 | \([1, 1, 0, 2240059406498, 34297233483693556]\) | \(8397215602029973870221522833066951/4862932275437849045190583664640\) | \(-719888502541234847652589227223860264960\) | \([]\) | \(14271409152\) | \(6.1455\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 301530p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 301530p do not have complex multiplication.Modular form 301530.2.a.p
sage: E.q_eigenform(10)