Show commands:
SageMath
E = EllipticCurve("lu1")
E.isogeny_class()
Elliptic curves in class 487872lu
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
487872.lu1 | 487872lu1 | \([0, 0, 0, -224422572, -1297179247408]\) | \(-30515071121161/85766121\) | \(-3513376563454874256408576\) | \([]\) | \(116785152\) | \(3.5822\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 487872lu1 has rank \(1\).
Complex multiplication
The elliptic curves in class 487872lu do not have complex multiplication.Modular form 487872.2.a.lu
sage: E.q_eigenform(10)