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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 4025.b
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 4025.b1 | 4025e1 | \([0, 1, 1, 575092, 300275344]\) | \(1346216501445963776/3268768272021875\) | \(-51074504250341796875\) | \([]\) | \(137280\) | \(2.4656\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4025.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4025.b do not have complex multiplication.Modular form 4025.2.a.b
sage: E.q_eigenform(10)