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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 190575.dp
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
190575.dp1 | 190575dn1 | \([1, -1, 0, -1715742, 23796343291]\) | \(-3025/1323\) | \(-244294825123561201171875\) | \([]\) | \(24330240\) | \(3.1668\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 190575.dp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 190575.dp do not have complex multiplication.Modular form 190575.2.a.dp
sage: E.q_eigenform(10)