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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 80850k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80850.f1 | 80850k1 | \([1, 1, 0, -8122825, 8833277125]\) | \(123865101442627825/1185257981952\) | \(567164464020000000000\) | \([]\) | \(4878720\) | \(2.8025\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80850k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 80850k do not have complex multiplication.Modular form 80850.2.a.k
sage: E.q_eigenform(10)