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Properties

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

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 2310.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.g1 2310h3 \([1, 0, 1, -864, -9764]\) \(71210194441849/631496250\) \(631496250\) \([2]\) \(2048\) \(0.51194\)  
2310.g2 2310h2 \([1, 0, 1, -94, 92]\) \(90458382169/48024900\) \(48024900\) \([2, 2]\) \(1024\) \(0.16537\)  
2310.g3 2310h1 \([1, 0, 1, -74, 236]\) \(43949604889/55440\) \(55440\) \([2]\) \(512\) \(-0.18121\) \(\Gamma_0(N)\)-optimal
2310.g4 2310h4 \([1, 0, 1, 356, 812]\) \(5009866738631/3163773690\) \(-3163773690\) \([2]\) \(2048\) \(0.51194\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2310.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.