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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 185020.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
185020.r1 | 185020p1 | \([0, -1, 0, -2310, 43805]\) | \(-101351846656/805255\) | \(-10835511280\) | \([]\) | \(180000\) | \(0.75375\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 185020.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 185020.r do not have complex multiplication.Modular form 185020.2.a.r
sage: E.q_eigenform(10)