Properties

Label 4704.c
Number of curves $4$
Conductor $4704$
CM no
Rank $1$
Graph

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

Elliptic curves in class 4704.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.c1 4704v3 \([0, -1, 0, -16529, 823425]\) \(1036433728/63\) \(30359089152\) \([4]\) \(6144\) \(1.0719\)  
4704.c2 4704v2 \([0, -1, 0, -5504, -145452]\) \(306182024/21609\) \(1301645947392\) \([2]\) \(6144\) \(1.0719\)  
4704.c3 4704v1 \([0, -1, 0, -1094, 11544]\) \(19248832/3969\) \(29884728384\) \([2, 2]\) \(3072\) \(0.72533\) \(\Gamma_0(N)\)-optimal
4704.c4 4704v4 \([0, -1, 0, 2336, 66424]\) \(23393656/45927\) \(-2766471998976\) \([2]\) \(6144\) \(1.0719\)  

Rank

sage: E.rank()
 

The elliptic curves in class 4704.c have rank \(1\).

Complex multiplication

The elliptic curves in class 4704.c do not have complex multiplication.

Modular form 4704.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{5} + q^{9} - 2 q^{13} + 2 q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.