Properties

Label 9464.c
Number of curves $4$
Conductor $9464$
CM no
Rank $0$
Graph

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

Elliptic curves in class 9464.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9464.c1 9464d4 \([0, 0, 0, -50531, 4372030]\) \(1443468546/7\) \(69197133824\) \([2]\) \(18432\) \(1.2804\)  
9464.c2 9464d3 \([0, 0, 0, -9971, -303186]\) \(11090466/2401\) \(23734616901632\) \([2]\) \(18432\) \(1.2804\)  
9464.c3 9464d2 \([0, 0, 0, -3211, 65910]\) \(740772/49\) \(242189968384\) \([2, 2]\) \(9216\) \(0.93387\)  
9464.c4 9464d1 \([0, 0, 0, 169, 4394]\) \(432/7\) \(-8649641728\) \([2]\) \(4608\) \(0.58729\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9464.c have rank \(0\).

Complex multiplication

The elliptic curves in class 9464.c do not have complex multiplication.

Modular form 9464.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + q^{7} - 3q^{9} + 4q^{11} - 6q^{17} - 8q^{19} + O(q^{20})\)  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.