Properties

Label 2310i
Number of curves 4
Conductor 2310
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2310.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.i3 2310i1 [1, 0, 1, -899, 10046] [6] 1728 \(\Gamma_0(N)\)-optimal
2310.i4 2310i2 [1, 0, 1, 181, 32942] [6] 3456  
2310.i1 2310i3 [1, 0, 1, -9314, -342988] [2] 5184  
2310.i2 2310i4 [1, 0, 1, -1634, -889804] [2] 10368  

Rank

sage: E.rank()
 

The elliptic curves in class 2310i have rank \(0\).

Modular form 2310.2.a.i

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.