Properties

Label 61710j
Number of curves $1$
Conductor $61710$
CM no
Rank $0$

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

Elliptic curves in class 61710j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
61710.r1 61710j1 \([1, 1, 0, -9571597, 11398786909]\) \(-72861639994809235116611/36094044206592000\) \(-48041172838973952000\) \([]\) \(4458240\) \(2.7298\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 61710j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 61710j do not have complex multiplication.

Modular form 61710.2.a.j

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 3 q^{7} - q^{8} + q^{9} - q^{10} - q^{12} + 3 q^{13} - 3 q^{14} - q^{15} + q^{16} - q^{17} - q^{18} - 3 q^{19} + O(q^{20})\) Copy content Toggle raw display