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SageMath
E = EllipticCurve("bz1")
E.isogeny_class()
Elliptic curves in class 117117.bz
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
117117.bz1 | 117117bv1 | \([0, 0, 1, -520550589, 3781031112589]\) | \(26232410028444086272/4795233247959077\) | \(2851570305471484821924592893\) | \([]\) | \(88957440\) | \(3.9868\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 117117.bz1 has rank \(0\).
Complex multiplication
The elliptic curves in class 117117.bz do not have complex multiplication.Modular form 117117.2.a.bz
sage: E.q_eigenform(10)