Properties

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

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

Elliptic curves in class 2310.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.k1 2310j4 \([1, 0, 1, -266113, 52815788]\) \(2084105208962185000201/31185000\) \(31185000\) \([2]\) \(12288\) \(1.4415\)  
2310.k2 2310j3 \([1, 0, 1, -18033, 676876]\) \(648474704552553481/176469171805080\) \(176469171805080\) \([2]\) \(12288\) \(1.4415\)  
2310.k3 2310j2 \([1, 0, 1, -16633, 824156]\) \(508859562767519881/62240270400\) \(62240270400\) \([2, 2]\) \(6144\) \(1.0950\)  
2310.k4 2310j1 \([1, 0, 1, -953, 15068]\) \(-95575628340361/43812679680\) \(-43812679680\) \([2]\) \(3072\) \(0.74838\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2310.2.a.k

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.