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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 284592.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
284592.j1 | 284592j1 | \([0, -1, 0, -110700, -14139684]\) | \(-8985792737264/2187\) | \(-36514291968\) | \([]\) | \(1548288\) | \(1.4039\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 284592.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 284592.j do not have complex multiplication.Modular form 284592.2.a.j
sage: E.q_eigenform(10)