Show commands:
SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 123627.u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123627.u1 | 123627w1 | \([1, 0, 1, -44917687232, -3329834430577147]\) | \(170295687079857398473/17163597526568829\) | \(1010137619486580640597189943315181\) | \([]\) | \(955468800\) | \(5.0691\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123627.u1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123627.u do not have complex multiplication.Modular form 123627.2.a.u
sage: E.q_eigenform(10)