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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 123210z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
123210.p1 | 123210z1 | \([1, -1, 0, -2261160, -83180862144]\) | \(-683565019129/1597684769280\) | \(-2988332842227301810414080\) | \([]\) | \(23639040\) | \(3.3754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123210z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123210z do not have complex multiplication.Modular form 123210.2.a.z
sage: E.q_eigenform(10)