Properties

Label 308763.e
Number of curves $6$
Conductor $308763$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("308763.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 308763.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
308763.e1 308763e4 [1, -1, 1, -311233136, -2113298604660] [2] 28311552  
308763.e2 308763e5 [1, -1, 1, -64595381, 162457932030] [2] 56623104  
308763.e3 308763e3 [1, -1, 1, -19824746, -31685449584] [2, 2] 28311552  
308763.e4 308763e2 [1, -1, 1, -19452101, -33016537524] [2, 2] 14155776  
308763.e5 308763e1 [1, -1, 1, -1192496, -536352150] [2] 7077888 \(\Gamma_0(N)\)-optimal
308763.e6 308763e6 [1, -1, 1, 18983569, -140643674778] [2] 56623104  

Rank

sage: E.rank()
 

The elliptic curves in class 308763.e have rank \(0\).

Modular form 308763.2.a.e

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} - 2q^{5} - q^{7} + 3q^{8} + 2q^{10} + 4q^{11} + q^{14} - q^{16} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.