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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 61347p
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 61347.ba1 | 61347p1 | \([0, -1, 1, -20619408, 57540131417]\) | \(-7744000000/6940323\) | \(-868893699819665570271507\) | \([]\) | \(14192640\) | \(3.2904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61347p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 61347p do not have complex multiplication.Modular form 61347.2.a.p
sage: E.q_eigenform(10)