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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 39675.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
39675.j1 | 39675u1 | \([1, 1, 1, -403638, -97797444]\) | \(78605490625/985527\) | \(91183353486564375\) | \([]\) | \(456192\) | \(2.0638\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 39675.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 39675.j do not have complex multiplication.Modular form 39675.2.a.j
sage: E.q_eigenform(10)