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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 20230.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20230.j1 | 20230i1 | \([1, 0, 1, -456193, 106503556]\) | \(1505139743881/168070000\) | \(1172415553108870000\) | \([]\) | \(391680\) | \(2.2001\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20230.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 20230.j do not have complex multiplication.Modular form 20230.2.a.j
sage: E.q_eigenform(10)