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SageMath
E = EllipticCurve("dp1")
E.isogeny_class()
Elliptic curves in class 141570dp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 141570.h1 | 141570dp1 | \([1, -1, 0, -516555, -151539899]\) | \(-172806866567322361/12654720000000\) | \(-1116260196480000000\) | \([]\) | \(2096640\) | \(2.2123\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 141570dp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 141570dp do not have complex multiplication.Modular form 141570.2.a.dp
sage: E.q_eigenform(10)