Properties

Label 4263g
Number of curves $6$
Conductor $4263$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4263.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4263g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4263.c5 4263g1 [1, 0, 0, -38417, -3106272] [2] 18432 \(\Gamma_0(N)\)-optimal
4263.c4 4263g2 [1, 0, 0, -626662, -190991725] [2, 2] 36864  
4263.c1 4263g3 [1, 0, 0, -10026577, -12221002942] [2] 73728  
4263.c3 4263g4 [1, 0, 0, -638667, -183296520] [2, 2] 73728  
4263.c2 4263g5 [1, 0, 0, -2080982, 939113013] [4] 147456  
4263.c6 4263g6 [1, 0, 0, 611568, -813164913] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 4263g have rank \(0\).

Modular form 4263.2.a.c

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} - q^{4} + 2q^{5} - q^{6} + 3q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} + 2q^{13} + 2q^{15} - q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.