Properties

Label 317900.e
Number of curves 4
Conductor 317900
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("317900.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 317900.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
317900.e1 317900e4 [0, 1, 0, -51299908, -141441034812] [2] 26873856  
317900.e2 317900e3 [0, 1, 0, -3217533, -2194476812] [2] 13436928  
317900.e3 317900e2 [0, 1, 0, -724908, -134484812] [2] 8957952  
317900.e4 317900e1 [0, 1, 0, -327533, 70560688] [2] 4478976 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 317900.e have rank \(1\).

Modular form 317900.2.a.e

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{13} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.