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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 250173r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
250173.r1 | 250173r1 | \([0, 0, 1, -2778978, -1473520685]\) | \(69203793903616/12699136989\) | \(435535281851063193261\) | \([]\) | \(7603200\) | \(2.6788\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 250173r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 250173r do not have complex multiplication.Modular form 250173.2.a.r
sage: E.q_eigenform(10)