Properties

Label 8400bl
Number of curves $6$
Conductor $8400$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("8400.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8400bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8400.k5 8400bl1 [0, -1, 0, -1608, -54288] [2] 12288 \(\Gamma_0(N)\)-optimal
8400.k4 8400bl2 [0, -1, 0, -33608, -2358288] [2, 2] 24576  
8400.k1 8400bl3 [0, -1, 0, -537608, -151542288] [2] 49152  
8400.k3 8400bl4 [0, -1, 0, -41608, -1142288] [2, 2] 49152  
8400.k2 8400bl5 [0, -1, 0, -365608, 84393712] [2] 98304  
8400.k6 8400bl6 [0, -1, 0, 154392, -8982288] [2] 98304  

Rank

sage: E.rank()
 

The elliptic curves in class 8400bl have rank \(0\).

Modular form 8400.2.a.k

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{7} + q^{9} + 4q^{11} - 6q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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 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.