Properties

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

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

Elliptic curves in class 2310k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.j4 2310k1 \([1, 0, 1, 192, -194]\) \(788632918919/475398000\) \(-475398000\) \([2]\) \(1536\) \(0.35423\) \(\Gamma_0(N)\)-optimal
2310.j3 2310k2 \([1, 0, 1, -788, -1762]\) \(54014438633401/30015562500\) \(30015562500\) \([2, 2]\) \(3072\) \(0.70080\)  
2310.j1 2310k3 \([1, 0, 1, -9538, -358762]\) \(95946737295893401/168104301750\) \(168104301750\) \([2]\) \(6144\) \(1.0474\)  
2310.j2 2310k4 \([1, 0, 1, -7718, 258806]\) \(50834334659676121/338378906250\) \(338378906250\) \([2]\) \(6144\) \(1.0474\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 2310k do not have complex multiplication.

Modular form 2310.2.a.k

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