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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 36414r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
36414.o1 | 36414r1 | \([1, -1, 0, -105, 557]\) | \(-610929/224\) | \(-47192544\) | \([]\) | \(10080\) | \(0.18281\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 36414r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 36414r do not have complex multiplication.Modular form 36414.2.a.r
sage: E.q_eigenform(10)