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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 12789j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12789.q1 | 12789j1 | \([0, 0, 1, -1029, 46219]\) | \(-4096/29\) | \(-853115605587\) | \([]\) | \(20160\) | \(0.97254\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12789j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12789j do not have complex multiplication.Modular form 12789.2.a.j
sage: E.q_eigenform(10)