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Properties

Label 40310.j
Number of curves $2$
Conductor $40310$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 40310.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
40310.j1 40310c1 \([1, 0, 1, -554854, 159228856]\) \(-18891165411761705909209/26828620509593600\) \(-26828620509593600\) \([3]\) \(370944\) \(2.0555\) \(\Gamma_0(N)\)-optimal
40310.j2 40310c2 \([1, 0, 1, 795531, 752817792]\) \(55679563269984774587831/277008210722816000000\) \(-277008210722816000000\) \([]\) \(1112832\) \(2.6048\)  

Rank

sage: E.rank()
 

The elliptic curves in class 40310.j have rank \(1\).

Complex multiplication

The elliptic curves in class 40310.j do not have complex multiplication.

Modular form 40310.2.a.j

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.