Properties

Label 113715t
Number of curves 4
Conductor 113715
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("113715.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 113715t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
113715.bd3 113715t1 [1, -1, 0, -8190, 272335] [2] 193536 \(\Gamma_0(N)\)-optimal
113715.bd2 113715t2 [1, -1, 0, -24435, -1127984] [2, 2] 387072  
113715.bd4 113715t3 [1, -1, 0, 56790, -7089899] [2] 774144  
113715.bd1 113715t4 [1, -1, 0, -365580, -84981425] [2] 774144  

Rank

sage: E.rank()
 

The elliptic curves in class 113715t have rank \(0\).

Modular form 113715.2.a.bd

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} - q^{5} + q^{7} - 3q^{8} - q^{10} + 6q^{13} + q^{14} - q^{16} - 2q^{17} + O(q^{20}) \)

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 Cremona 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 Cremona labels.