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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4650j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4650.f1 | 4650j1 | \([1, 1, 0, -2700, 54000]\) | \(-1115157653/26784\) | \(-52312500000\) | \([]\) | \(7200\) | \(0.84260\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4650j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4650j do not have complex multiplication.Modular form 4650.2.a.j
sage: E.q_eigenform(10)