Properties

Label 310464.pq
Number of curves 6
Conductor 310464
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("310464.pq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 310464.pq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
310464.pq1 310464pq5 [0, 0, 0, -127544844, 554424316432] [2] 31457280  
310464.pq2 310464pq3 [0, 0, 0, -8016204, 8560923280] [2, 2] 15728640  
310464.pq3 310464pq2 [0, 0, 0, -1101324, -248633840] [2, 2] 7864320  
310464.pq4 310464pq1 [0, 0, 0, -960204, -362037872] [2] 3932160 \(\Gamma_0(N)\)-optimal
310464.pq5 310464pq6 [0, 0, 0, 874356, 26509185808] [2] 31457280  
310464.pq6 310464pq4 [0, 0, 0, 3555636, -1800332912] [2] 15728640  

Rank

sage: E.rank()
 

The elliptic curves in class 310464.pq have rank \(1\).

Modular form 310464.2.a.pq

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + q^{11} + 6q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.