Show commands:
SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 100027.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100027.a1 | 100027a1 | \([1, -1, 1, 2, -16]\) | \(1367631/100027\) | \(-100027\) | \([]\) | \(14088\) | \(-0.36102\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100027.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100027.a do not have complex multiplication.Modular form 100027.2.a.a
sage: E.q_eigenform(10)