Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("2310.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.k4 2310j1 [1, 0, 1, -953, 15068] [2] 3072 \(\Gamma_0(N)\)-optimal
2310.k3 2310j2 [1, 0, 1, -16633, 824156] [2, 2] 6144  
2310.k2 2310j3 [1, 0, 1, -18033, 676876] [2] 12288  
2310.k1 2310j4 [1, 0, 1, -266113, 52815788] [2] 12288  

Rank

sage: E.rank()
 

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

Modular form 2310.2.a.k

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

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.