Properties

Label 31850.cn
Number of curves $2$
Conductor $31850$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cn1")
 
E.isogeny_class()
 

Elliptic curves in class 31850.cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31850.cn1 31850cj2 \([1, 1, 1, -13879888, 19897607281]\) \(-6434774386429585/140608\) \(-6461871325000000\) \([]\) \(1263600\) \(2.5601\)  
31850.cn2 31850cj1 \([1, 1, 1, -159888, 31047281]\) \(-9836106385/3407872\) \(-156614348800000000\) \([]\) \(421200\) \(2.0108\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 31850.cn have rank \(0\).

Complex multiplication

The elliptic curves in class 31850.cn do not have complex multiplication.

Modular form 31850.2.a.cn

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.