Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 51600.u
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 51600.u1 | 51600bp1 | \([0, -1, 0, -17649608, -28534422288]\) | \(-9500554530751882177/199908972324\) | \(-12794174228736000000\) | \([]\) | \(1969920\) | \(2.7843\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51600.u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51600.u do not have complex multiplication.Modular form 51600.2.a.u
sage: E.q_eigenform(10)