Properties

Label 5610.k
Number of curves $1$
Conductor $5610$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.k1 5610l1 \([1, 0, 1, -2864, -71938]\) \(-2596717791529849/718080000000\) \(-718080000000\) \([]\) \(14112\) \(0.99076\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 5610.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 5610.k do not have complex multiplication.

Modular form 5610.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 3 q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} - 5 q^{13} + 3 q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + 7 q^{19} + O(q^{20})\) Copy content Toggle raw display