Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4704.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4704.m1 4704u3 \([0, -1, 0, -10992, 447252]\) \(2438569736/21\) \(1264962048\) \([4]\) \(6144\) \(0.91432\)  
4704.m2 4704u2 \([0, -1, 0, -2417, -37407]\) \(3241792/567\) \(273231802368\) \([2]\) \(6144\) \(0.91432\)  
4704.m3 4704u1 \([0, -1, 0, -702, 6840]\) \(5088448/441\) \(3320525376\) \([2, 2]\) \(3072\) \(0.56775\) \(\Gamma_0(N)\)-optimal
4704.m4 4704u4 \([0, -1, 0, 768, 30360]\) \(830584/7203\) \(-433881982464\) \([2]\) \(6144\) \(0.91432\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 4704.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2q^{5} + q^{9} - 4q^{11} + 6q^{13} - 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20})\)  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.