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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 75810.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75810.r1 | 75810s1 | \([1, 1, 0, -466742, 125141076]\) | \(-1639438054438062619/40650200801280\) | \(-278819727295979520\) | \([]\) | \(1456000\) | \(2.1322\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75810.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 75810.r do not have complex multiplication.Modular form 75810.2.a.r
sage: E.q_eigenform(10)