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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 139587r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139587.r1 | 139587r1 | \([0, -1, 1, -27840, -2077153]\) | \(-98867482624/20696067\) | \(-499552745241123\) | \([]\) | \(1555200\) | \(1.5421\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139587r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 139587r do not have complex multiplication.Modular form 139587.2.a.r
sage: E.q_eigenform(10)