Properties

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

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

Elliptic curves in class 2310.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.i1 2310i3 \([1, 0, 1, -9314, -342988]\) \(89343998142858649/1112702976000\) \(1112702976000\) \([2]\) \(5184\) \(1.1212\)  
2310.i2 2310i4 \([1, 0, 1, -1634, -889804]\) \(-482056280171929/341652696000000\) \(-341652696000000\) \([2]\) \(10368\) \(1.4678\)  
2310.i3 2310i1 \([1, 0, 1, -899, 10046]\) \(80224711835689/2173469760\) \(2173469760\) \([6]\) \(1728\) \(0.57191\) \(\Gamma_0(N)\)-optimal
2310.i4 2310i2 \([1, 0, 1, 181, 32942]\) \(661003929431/468755040600\) \(-468755040600\) \([6]\) \(3456\) \(0.91848\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2310.2.a.i

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.