Properties

Label 4900.e
Number of curves 4
Conductor 4900
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("4900.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4900.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4900.e1 4900k3 [0, 1, 0, -50633, 4367488] [2] 12960  
4900.e2 4900k4 [0, 1, 0, -44508, 5469988] [2] 25920  
4900.e3 4900k1 [0, 1, 0, -1633, -18012] [2] 4320 \(\Gamma_0(N)\)-optimal
4900.e4 4900k2 [0, 1, 0, 4492, -116012] [2] 8640  

Rank

sage: E.rank()
 

The elliptic curves in class 4900.e have rank \(1\).

Modular form 4900.2.a.e

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.