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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 192027.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
192027.r1 | 192027t1 | \([0, -1, 1, 1940, -6843]\) | \(45056/27\) | \(-483633249363\) | \([]\) | \(453024\) | \(0.93134\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 192027.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 192027.r do not have complex multiplication.Modular form 192027.2.a.r
sage: E.q_eigenform(10)