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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 16744.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
16744.j1 | 16744i1 | \([0, -1, 0, -169, -195]\) | \(2097544192/1107197\) | \(283442432\) | \([]\) | \(4416\) | \(0.31344\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 16744.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 16744.j do not have complex multiplication.Modular form 16744.2.a.j
sage: E.q_eigenform(10)