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Properties

Label 11310.c
Number of curves $4$
Conductor $11310$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 11310.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11310.c1 11310c3 \([1, 1, 0, -8352, -272484]\) \(64443098670429961/6032611833300\) \(6032611833300\) \([2]\) \(49152\) \(1.1907\)  
11310.c2 11310c2 \([1, 1, 0, -1852, 25216]\) \(703093388853961/115124490000\) \(115124490000\) \([2, 2]\) \(24576\) \(0.84417\)  
11310.c3 11310c1 \([1, 1, 0, -1772, 27984]\) \(615882348586441/21715200\) \(21715200\) \([2]\) \(12288\) \(0.49759\) \(\Gamma_0(N)\)-optimal
11310.c4 11310c4 \([1, 1, 0, 3368, 147364]\) \(4223169036960119/11647532812500\) \(-11647532812500\) \([4]\) \(49152\) \(1.1907\)  

Rank

sage: E.rank()
 

The elliptic curves in class 11310.c have rank \(2\).

Complex multiplication

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

Modular form 11310.2.a.c

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.