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SageMath
E = EllipticCurve("gw1")
E.isogeny_class()
Elliptic curves in class 69696.gw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
69696.gw1 | 69696dn1 | \([0, 0, 0, 132, -110]\) | \(45056/27\) | \(-152425152\) | \([]\) | \(23040\) | \(0.25947\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 69696.gw1 has rank \(1\).
Complex multiplication
The elliptic curves in class 69696.gw do not have complex multiplication.Modular form 69696.2.a.gw
sage: E.q_eigenform(10)