Properties

Label 2310c
Number of curves 4
Conductor 2310
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2310.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.c3 2310c1 [1, 1, 0, -863, -10107] [2] 1536 \(\Gamma_0(N)\)-optimal
2310.c2 2310c2 [1, 1, 0, -1183, -2363] [2, 2] 3072  
2310.c1 2310c3 [1, 1, 0, -12183, 510237] [2] 6144  
2310.c4 2310c4 [1, 1, 0, 4697, -12947] [2] 6144  

Rank

sage: E.rank()
 

The elliptic curves in class 2310c have rank \(1\).

Modular form 2310.2.a.c

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.