Properties

Label 7056.ca
Number of curves $2$
Conductor $7056$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7056.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7056.ca

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7056.ca1 7056cc2 [0, 0, 0, -19803, 1043210] [2] 24576  
7056.ca2 7056cc1 [0, 0, 0, 357, 55370] [2] 12288 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 7056.2.a.ca

sage: E.q_eigenform(10)
 
\( q + 4q^{5} - 4q^{11} - 4q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.