Properties

Label 4950o
Number of curves 4
Conductor 4950
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4950.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4950o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4950.g3 4950o1 [1, -1, 0, -1242, -15584] [2] 4608 \(\Gamma_0(N)\)-optimal
4950.g4 4950o2 [1, -1, 0, 1008, -67334] [2] 9216  
4950.g1 4950o3 [1, -1, 0, -18117, 939541] [2] 13824  
4950.g2 4950o4 [1, -1, 0, -9117, 1866541] [2] 27648  

Rank

sage: E.rank()
 

The elliptic curves in class 4950o have rank \(1\).

Modular form 4950.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - 2q^{7} - q^{8} + q^{11} + 4q^{13} + 2q^{14} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.