Properties

Label 2310.l
Number of curves $8$
Conductor $2310$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2310.l1 2310l7 \([1, 0, 1, -256428, 46871746]\) \(1864737106103260904761/129177711985836360\) \(129177711985836360\) \([2]\) \(27648\) \(2.0313\)  
2310.l2 2310l4 \([1, 0, 1, -252003, 48670756]\) \(1769857772964702379561/691787250\) \(691787250\) \([6]\) \(9216\) \(1.4820\)  
2310.l3 2310l6 \([1, 0, 1, -50628, -3508094]\) \(14351050585434661561/3001282273281600\) \(3001282273281600\) \([2, 2]\) \(13824\) \(1.6847\)  
2310.l4 2310l3 \([1, 0, 1, -47748, -4019582]\) \(12038605770121350841/757333463040\) \(757333463040\) \([2]\) \(6912\) \(1.3381\)  
2310.l5 2310l2 \([1, 0, 1, -15753, 759256]\) \(432288716775559561/270140062500\) \(270140062500\) \([2, 6]\) \(4608\) \(1.1354\)  
2310.l6 2310l5 \([1, 0, 1, -12783, 1055068]\) \(-230979395175477481/348191894531250\) \(-348191894531250\) \([6]\) \(9216\) \(1.4820\)  
2310.l7 2310l1 \([1, 0, 1, -1173, 6928]\) \(178272935636041/81841914000\) \(81841914000\) \([6]\) \(2304\) \(0.78883\) \(\Gamma_0(N)\)-optimal
2310.l8 2310l8 \([1, 0, 1, 109092, -21141182]\) \(143584693754978072519/276341298967965000\) \(-276341298967965000\) \([2]\) \(27648\) \(2.0313\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 2310.2.a.l

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

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.