Properties

Label 140790.e
Number of curves $3$
Conductor $140790$
CM no
Rank $0$
Graph

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

Elliptic curves in class 140790.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
140790.e1 140790cu3 \([1, 1, 0, -75137103, 251879496807]\) \(-997161390145682805889/5653381347656250\) \(-265968306129455566406250\) \([]\) \(25194240\) \(3.3369\)  
140790.e2 140790cu1 \([1, 1, 0, -290973, -102232323]\) \(-57911193276769/62229772800\) \(-2927654485805836800\) \([]\) \(2799360\) \(2.2383\) \(\Gamma_0(N)\)-optimal
140790.e3 140790cu2 \([1, 1, 0, 2438187, 1842567093]\) \(34072410714499871/50858627625000\) \(-2392688943069062625000\) \([]\) \(8398080\) \(2.7876\)  

Rank

sage: E.rank()
 

The elliptic curves in class 140790.e have rank \(0\).

Complex multiplication

The elliptic curves in class 140790.e do not have complex multiplication.

Modular form 140790.2.a.e

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

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.