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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 392784.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
392784.j1 | 392784j1 | \([0, -1, 0, -5749, -177155]\) | \(-43614208/3507\) | \(-1689989296128\) | \([]\) | \(497664\) | \(1.0928\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 392784.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 392784.j do not have complex multiplication.Modular form 392784.2.a.j
sage: E.q_eigenform(10)