Show commands:
SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 8085.i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8085.i1 | 8085b1 | \([0, -1, 1, -3201, -67873]\) | \(12845056/165\) | \(46608416085\) | \([]\) | \(6720\) | \(0.85560\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8085.i1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8085.i do not have complex multiplication.Modular form 8085.2.a.i
sage: E.q_eigenform(10)