Properties

Label 4356.c
Number of curves $2$
Conductor $4356$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4356.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4356.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4356.c1 4356g2 [0, 0, 0, -1407351, 642598814] [2] 57600  
4356.c2 4356g1 [0, 0, 0, -84216, 10934165] [2] 28800 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4356.c have rank \(0\).

Modular form 4356.2.a.c

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 2q^{7} - 6q^{13} - 4q^{17} + 2q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.