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SageMath
E = EllipticCurve("m1")
E.isogeny_class()
Elliptic curves in class 428400.m
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 428400.m1 | 428400m1 | \([0, 0, 0, -26623875, 53298601225]\) | \(-286292506333578400000/2661667281642663\) | \(-19403554483175013270000\) | \([]\) | \(40550400\) | \(3.0986\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 428400.m1 has rank \(1\).
Complex multiplication
The elliptic curves in class 428400.m do not have complex multiplication.Modular form 428400.2.a.m
sage: E.q_eigenform(10)