Properties

Label 7056.bd
Number of curves 6
Conductor 7056
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("7056.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bd1 7056bp6 [0, 0, 0, -19266555, 32550241066] [2] 165888  
7056.bd2 7056bp5 [0, 0, 0, -1203195, 509453098] [2] 82944  
7056.bd3 7056bp4 [0, 0, 0, -250635, 39587002] [2] 55296  
7056.bd4 7056bp2 [0, 0, 0, -74235, -7779926] [2] 18432  
7056.bd5 7056bp1 [0, 0, 0, -3675, -173558] [2] 9216 \(\Gamma_0(N)\)-optimal
7056.bd6 7056bp3 [0, 0, 0, 31605, 3629626] [2] 27648  

Rank

sage: E.rank()
 

The elliptic curves in class 7056.bd have rank \(0\).

Modular form 7056.2.a.bd

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.