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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 81627x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
81627.b1 | 81627x1 | \([0, 1, 1, -16280, -938440]\) | \(-98867482624/20696067\) | \(-99895962460203\) | \([]\) | \(691200\) | \(1.4080\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 81627x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 81627x do not have complex multiplication.Modular form 81627.2.a.x
sage: E.q_eigenform(10)