Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 77a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
77.a1 | 77a1 | \([0, 0, 1, 2, 0]\) | \(884736/539\) | \(-539\) | \([]\) | \(4\) | \(-0.78665\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 77a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 77a do not have complex multiplication.Modular form 77.2.a.a
sage: E.q_eigenform(10)