Properties

Label 346560ef
Number of curves $4$
Conductor $346560$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("346560.ef1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 346560ef

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.ef3 346560ef1 [0, -1, 0, -716705, -231902175] [2] 4423680 \(\Gamma_0(N)\)-optimal
346560.ef2 346560ef2 [0, -1, 0, -1178785, 104214817] [2, 2] 8847360  
346560.ef1 346560ef3 [0, -1, 0, -14348065, 20893240225] [2] 17694720  
346560.ef4 346560ef4 [0, -1, 0, 4597215, 819283617] [2] 17694720  

Rank

sage: E.rank()
 

The elliptic curves in class 346560ef have rank \(1\).

Modular form 346560.2.a.ef

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + q^{9} - 4q^{11} + 2q^{13} - q^{15} + 2q^{17} + O(q^{20}) \)

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.