Properties

Label 11310e
Number of curves $4$
Conductor $11310$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 11310e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11310.d2 11310e1 \([1, 0, 1, -4170829, 3278200952]\) \(8023996232564328604273609/2693913066000\) \(2693913066000\) \([6]\) \(214272\) \(2.1809\) \(\Gamma_0(N)\)-optimal
11310.d3 11310e2 \([1, 0, 1, -4170249, 3279158416]\) \(-8020649220830773808798089/4649360115706312500\) \(-4649360115706312500\) \([6]\) \(428544\) \(2.5275\)  
11310.d1 11310e3 \([1, 0, 1, -4240444, 3163087226]\) \(8432523527010257294720569/556754628456000000000\) \(556754628456000000000\) \([2]\) \(642816\) \(2.7302\)  
11310.d4 11310e4 \([1, 0, 1, 3564036, 13489975162]\) \(5006683449688877689783751/81509038330078125000000\) \(-81509038330078125000000\) \([2]\) \(1285632\) \(3.0768\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11310e have rank \(1\).

Complex multiplication

The elliptic curves in class 11310e do not have complex multiplication.

Modular form 11310.2.a.e

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