Properties

Label 31433.b
Number of curves $4$
Conductor $31433$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 31433.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
31433.b1 31433b4 \([1, -1, 0, -167681, 26470544]\) \(82483294977/17\) \(107463171833\) \([2]\) \(80640\) \(1.5040\)  
31433.b2 31433b2 \([1, -1, 0, -10516, 412587]\) \(20346417/289\) \(1826873921161\) \([2, 2]\) \(40320\) \(1.1574\)  
31433.b3 31433b1 \([1, -1, 0, -1271, -7136]\) \(35937/17\) \(107463171833\) \([2]\) \(20160\) \(0.81082\) \(\Gamma_0(N)\)-optimal
31433.b4 31433b3 \([1, -1, 0, -1271, 1105962]\) \(-35937/83521\) \(-527966563215529\) \([2]\) \(80640\) \(1.5040\)  

Rank

sage: E.rank()
 

The elliptic curves in class 31433.b have rank \(1\).

Complex multiplication

The elliptic curves in class 31433.b do not have complex multiplication.

Modular form 31433.2.a.b

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