Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 139.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139.a1 | 139a1 | \([1, 1, 0, -3, -4]\) | \(-4826809/139\) | \(-139\) | \([]\) | \(6\) | \(-0.80932\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139.a1 has rank \(0\).
Complex multiplication
The elliptic curves in class 139.a do not have complex multiplication.Modular form 139.2.a.a
sage: E.q_eigenform(10)