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Properties

Label 244758.e
Number of curves $2$
Conductor $244758$
CM no
Rank $0$
Graph

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

Elliptic curves in class 244758.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
244758.e1 244758e2 \([1, 1, 0, -2570688, 17604675804]\) \(-39934705050538129/2823126576537804\) \(-132816476967734918985324\) \([]\) \(23115456\) \(3.1167\)  
244758.e2 244758e1 \([1, 1, 0, -599628, -180198576]\) \(-506814405937489/4048994304\) \(-190488504195661824\) \([]\) \(3302208\) \(2.1437\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 244758.e have rank \(0\).

Complex multiplication

The elliptic curves in class 244758.e do not have complex multiplication.

Modular form 244758.2.a.e

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.