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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 134640dp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
134640.k1 | 134640dp1 | \([0, 0, 0, -243, 18738]\) | \(-19683/1870\) | \(-150762332160\) | \([]\) | \(142848\) | \(0.82449\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 134640dp1 has rank \(2\).
Complex multiplication
The elliptic curves in class 134640dp do not have complex multiplication.Modular form 134640.2.a.dp
sage: E.q_eigenform(10)