Properties

Label 51600.j
Number of curves $1$
Conductor $51600$
CM no
Rank $2$

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Show commands for: SageMath
sage: E = EllipticCurve("j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 51600.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.j1 51600cm1 \([0, -1, 0, 667, 6537]\) \(327680/387\) \(-38700000000\) \([]\) \(37440\) \(0.71785\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 51600.j1 has rank \(2\).

Complex multiplication

The elliptic curves in class 51600.j do not have complex multiplication.

Modular form 51600.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2q^{7} + q^{9} - q^{11} + 3q^{13} - q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display