Properties

Label 7056.bb
Number of curves $4$
Conductor $7056$
CM -3
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7056.bb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.bb1 7056bf4 [0, 0, 0, -6615, -203742] [2] 6912  
7056.bb2 7056bf2 [0, 0, 0, -735, 7546] [2] 2304  
7056.bb3 7056bf3 [0, 0, 0, 0, -9261] [2] 3456  
7056.bb4 7056bf1 [0, 0, 0, 0, 343] [2] 1152 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7056.bb have rank \(1\).

Modular form 7056.2.a.bb

sage: E.q_eigenform(10)
 
\( q - 2q^{13} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.