Properties

Label 5610.t
Number of curves $4$
Conductor $5610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("t1")
 
E.isogeny_class()
 

Elliptic curves in class 5610.t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5610.t1 5610r4 \([1, 0, 1, -2417353, -1087483252]\) \(1562225332123379392365961/393363080510106009600\) \(393363080510106009600\) \([2]\) \(276480\) \(2.6617\)  
5610.t2 5610r2 \([1, 0, 1, -829978, 290863148]\) \(63229930193881628103961/26218934428500000\) \(26218934428500000\) \([6]\) \(92160\) \(2.1124\)  
5610.t3 5610r1 \([1, 0, 1, -43898, 5987756]\) \(-9354997870579612441/10093752054144000\) \(-10093752054144000\) \([6]\) \(46080\) \(1.7658\) \(\Gamma_0(N)\)-optimal
5610.t4 5610r3 \([1, 0, 1, 367927, -108178804]\) \(5508208700580085578359/8246033269590589440\) \(-8246033269590589440\) \([2]\) \(138240\) \(2.3151\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5610.t have rank \(0\).

Complex multiplication

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

Modular form 5610.2.a.t

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.