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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 50025c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 50025.m1 | 50025c1 | \([0, -1, 1, -2605193533, 16913745257718]\) | \(125147927114815865709295304704/64514985611316331088611125\) | \(1008046650176817673259548828125\) | \([]\) | \(51367680\) | \(4.4492\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 50025c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 50025c do not have complex multiplication.Modular form 50025.2.a.c
sage: E.q_eigenform(10)