Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 9072.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
9072.r1 | 9072e1 | \([0, 0, 0, 81, -243]\) | \(6912/7\) | \(-59521392\) | \([]\) | \(1728\) | \(0.17869\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 9072.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 9072.r do not have complex multiplication.Modular form 9072.2.a.r
sage: E.q_eigenform(10)