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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 704.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
704.j1 | 704c1 | \([0, 1, 0, 1, -1]\) | \(512/11\) | \(-704\) | \([]\) | \(32\) | \(-0.77330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 704.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 704.j do not have complex multiplication.Modular form 704.2.a.j
sage: E.q_eigenform(10)