Show commands:
SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 19008.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19008.r1 | 19008k1 | \([0, 0, 0, -36, -86]\) | \(-2985984/121\) | \(-209088\) | \([]\) | \(1920\) | \(-0.21128\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19008.r1 has rank \(0\).
Complex multiplication
The elliptic curves in class 19008.r do not have complex multiplication.Modular form 19008.2.a.r
sage: E.q_eigenform(10)