Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 71478a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
71478.g1 | 71478a1 | \([1, -1, 0, 798645, -85857211]\) | \(8869743/5632\) | \(-35771433732723009024\) | \([]\) | \(2298240\) | \(2.4410\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 71478a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 71478a do not have complex multiplication.Modular form 71478.2.a.a
sage: E.q_eigenform(10)