Properties

Label 2310.b
Number of curves $4$
Conductor $2310$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.b1 2310b3 \([1, 1, 0, -2990738, 1982276532]\) \(2958414657792917260183849/12401051653985258880\) \(12401051653985258880\) \([2]\) \(100352\) \(2.5184\)  
2310.b2 2310b2 \([1, 1, 0, -280338, -3362508]\) \(2436531580079063806249/1405478914998681600\) \(1405478914998681600\) \([2, 2]\) \(50176\) \(2.1718\)  
2310.b3 2310b1 \([1, 1, 0, -198418, -34016972]\) \(863913648706111516969/2486234429521920\) \(2486234429521920\) \([2]\) \(25088\) \(1.8252\) \(\Gamma_0(N)\)-optimal
2310.b4 2310b4 \([1, 1, 0, 1119342, -25477452]\) \(155099895405729262880471/90047655797243760000\) \(-90047655797243760000\) \([2]\) \(100352\) \(2.5184\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2310.2.a.b

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 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.