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SageMath
sage: E = EllipticCurve("j1")
sage: E.isogeny_class()
Elliptic curves in class 4704.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4704.j1 | 4704r1 | \([0, -1, 0, -93, -1035]\) | \(-448000/2187\) | \(-438939648\) | \([]\) | \(1344\) | \(0.34282\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4704.j1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4704.j do not have complex multiplication.Modular form 4704.2.a.j
sage: E.q_eigenform(10)