Properties

Label 308550.iz
Number of curves $8$
Conductor $308550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("iz1")
 
E.isogeny_class()
 

Elliptic curves in class 308550.iz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.iz1 308550iz7 \([1, 0, 0, -343246813, 2447657710367]\) \(161572377633716256481/914742821250\) \(25320667299319863281250\) \([2]\) \(62914560\) \(3.4904\)  
308550.iz2 308550iz4 \([1, 0, 0, -65824063, -205559111383]\) \(1139466686381936641/4080\) \(112937013750000\) \([2]\) \(15728640\) \(2.7973\)  
308550.iz3 308550iz5 \([1, 0, 0, -21840563, 36789429117]\) \(41623544884956481/2962701562500\) \(82009477230688476562500\) \([2, 2]\) \(31457280\) \(3.1438\)  
308550.iz4 308550iz3 \([1, 0, 0, -4356063, -2812963383]\) \(330240275458561/67652010000\) \(1872650976368906250000\) \([2, 2]\) \(15728640\) \(2.7973\)  
308550.iz5 308550iz2 \([1, 0, 0, -4114063, -3212021383]\) \(278202094583041/16646400\) \(460783016100000000\) \([2, 2]\) \(7864320\) \(2.4507\)  
308550.iz6 308550iz1 \([1, 0, 0, -242063, -56341383]\) \(-56667352321/16711680\) \(-462590008320000000\) \([2]\) \(3932160\) \(2.1041\) \(\Gamma_0(N)\)-optimal
308550.iz7 308550iz6 \([1, 0, 0, 9256437, -16874675883]\) \(3168685387909439/6278181696900\) \(-173784091330341576562500\) \([2]\) \(31457280\) \(3.1438\)  
308550.iz8 308550iz8 \([1, 0, 0, 19813687, 160544205867]\) \(31077313442863199/420227050781250\) \(-11632153973579406738281250\) \([2]\) \(62914560\) \(3.4904\)  

Rank

sage: E.rank()
 

The elliptic curves in class 308550.iz have rank \(1\).

Complex multiplication

The elliptic curves in class 308550.iz do not have complex multiplication.

Modular form 308550.2.a.iz

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + q^{12} - 2 q^{13} + q^{16} + q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 2 & 4 & 8 & 16 & 8 & 4 \\ 16 & 1 & 8 & 4 & 2 & 4 & 8 & 16 \\ 2 & 8 & 1 & 2 & 4 & 8 & 4 & 2 \\ 4 & 4 & 2 & 1 & 2 & 4 & 2 & 4 \\ 8 & 2 & 4 & 2 & 1 & 2 & 4 & 8 \\ 16 & 4 & 8 & 4 & 2 & 1 & 8 & 16 \\ 8 & 8 & 4 & 2 & 4 & 8 & 1 & 8 \\ 4 & 16 & 2 & 4 & 8 & 16 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.