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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 15680.dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 15680.dp1 | 15680y1 | \([0, 0, 0, 366422, -83755798]\) | \(722603599520256/820654296875\) | \(-6179146071875000000\) | \([]\) | \(506880\) | \(2.2921\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 15680.dp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 15680.dp do not have complex multiplication.Modular form 15680.2.a.dp
sage: E.q_eigenform(10)