Show commands:
SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 10115.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10115.k1 | 10115c1 | \([1, 0, 1, -72979, -3670469]\) | \(6161940649/2734375\) | \(19074336752734375\) | \([]\) | \(88128\) | \(1.8196\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10115.k1 has rank \(2\).
Complex multiplication
The elliptic curves in class 10115.k do not have complex multiplication.Modular form 10115.2.a.k
sage: E.q_eigenform(10)