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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 51800r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51800.x1 | 51800r1 | \([0, -1, 0, -15008, 716012]\) | \(-11683450802/63455\) | \(-2030560000000\) | \([]\) | \(135936\) | \(1.2055\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51800r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 51800r do not have complex multiplication.Modular form 51800.2.a.r
sage: E.q_eigenform(10)