Properties

Label 2352.i
Number of curves $6$
Conductor $2352$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2352.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2352.i1 2352c5 \([0, -1, 0, -18832, -988448]\) \(3065617154/9\) \(2168506368\) \([2]\) \(3072\) \(1.0208\)  
2352.i2 2352c4 \([0, -1, 0, -3152, 69168]\) \(28756228/3\) \(361417728\) \([2]\) \(1536\) \(0.67418\)  
2352.i3 2352c3 \([0, -1, 0, -1192, -14720]\) \(1556068/81\) \(9758278656\) \([2, 2]\) \(1536\) \(0.67418\)  
2352.i4 2352c2 \([0, -1, 0, -212, 960]\) \(35152/9\) \(271063296\) \([2, 2]\) \(768\) \(0.32760\)  
2352.i5 2352c1 \([0, -1, 0, 33, 78]\) \(2048/3\) \(-5647152\) \([2]\) \(384\) \(-0.018971\) \(\Gamma_0(N)\)-optimal
2352.i6 2352c6 \([0, -1, 0, 768, -60192]\) \(207646/6561\) \(-1580841142272\) \([2]\) \(3072\) \(1.0208\)  

Rank

sage: E.rank()
 

The elliptic curves in class 2352.i have rank \(0\).

Complex multiplication

The elliptic curves in class 2352.i do not have complex multiplication.

Modular form 2352.2.a.i

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.