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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 6762.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6762.j1 | 6762i1 | \([1, 1, 0, -81, -363]\) | \(-174676879/35328\) | \(-12117504\) | \([]\) | \(2880\) | \(0.081691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6762.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6762.j do not have complex multiplication.Modular form 6762.2.a.j
sage: E.q_eigenform(10)