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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 3904j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3904.b1 | 3904j1 | \([0, 1, 0, -129, -641]\) | \(-912673/61\) | \(-15990784\) | \([]\) | \(1024\) | \(0.13426\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3904j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 3904j do not have complex multiplication.Modular form 3904.2.a.j
sage: E.q_eigenform(10)