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SageMath
E = EllipticCurve("dj1")
E.isogeny_class()
Elliptic curves in class 47040dj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47040.fy1 | 47040dj1 | \([0, 1, 0, -14625, -685665]\) | \(-215474070728/3645\) | \(-5852528640\) | \([]\) | \(50688\) | \(1.0042\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47040dj1 has rank \(0\).
Complex multiplication
The elliptic curves in class 47040dj do not have complex multiplication.Modular form 47040.2.a.dj
sage: E.q_eigenform(10)