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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 29624.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
29624.j1 | 29624c1 | \([0, 1, 0, -84, 305]\) | \(-340736/49\) | \(-9538928\) | \([]\) | \(4608\) | \(0.069922\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 29624.j1 has rank \(2\).
Complex multiplication
The elliptic curves in class 29624.j do not have complex multiplication.Modular form 29624.2.a.j
sage: E.q_eigenform(10)