Properties

Label 44400.r
Number of curves $6$
Conductor $44400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("44400.r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 44400.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
44400.r1 44400x4 [0, -1, 0, -136402008, -613122217488] [2] 3981312  
44400.r2 44400x6 [0, -1, 0, -121250008, 511696982512] [2] 7962624  
44400.r3 44400x3 [0, -1, 0, -11730008, -1732777488] [2, 2] 3981312  
44400.r4 44400x2 [0, -1, 0, -8530008, -9566377488] [2, 2] 1990656  
44400.r5 44400x1 [0, -1, 0, -338008, -260265488] [2] 995328 \(\Gamma_0(N)\)-optimal
44400.r6 44400x5 [0, -1, 0, 46589992, -13863337488] [2] 7962624  

Rank

sage: E.rank()
 

The elliptic curves in class 44400.r have rank \(0\).

Modular form 44400.2.a.r

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.