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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 4900.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4900.j1 | 4900r1 | \([0, 0, 0, -6125, -214375]\) | \(-34560/7\) | \(-5147143750000\) | \([]\) | \(8640\) | \(1.1616\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4900.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4900.j do not have complex multiplication.Modular form 4900.2.a.j
sage: E.q_eigenform(10)