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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 109554.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
109554.j1 | 109554k1 | \([1, 0, 1, -259475, -51587422]\) | \(-2010409280180424553/31887805608612\) | \(-30644181189876132\) | \([]\) | \(1354320\) | \(1.9646\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 109554.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 109554.j do not have complex multiplication.Modular form 109554.2.a.j
sage: E.q_eigenform(10)