Properties

Label 344850.gz
Number of curves $4$
Conductor $344850$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("344850.gz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 344850.gz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
344850.gz1 344850gz3 [1, 0, 0, -1878588, 989452542] [2] 7864320  
344850.gz2 344850gz2 [1, 0, 0, -154338, 4905792] [2, 2] 3932160  
344850.gz3 344850gz1 [1, 0, 0, -93838, -11005708] [2] 1966080 \(\Gamma_0(N)\)-optimal
344850.gz4 344850gz4 [1, 0, 0, 601912, 38937042] [2] 7864320  

Rank

sage: E.rank()
 

The elliptic curves in class 344850.gz have rank \(1\).

Modular form 344850.2.a.gz

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} + 2q^{13} + q^{16} + 2q^{17} + q^{18} + q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.