Properties

Label 308550.h
Number of curves $8$
Conductor $308550$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 308550.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
308550.h1 308550h7 \([1, 1, 0, -608740359625, 182808192998717125]\) \(901247067798311192691198986281/552431869440\) \(15291668047765560000000\) \([2]\) \(1911029760\) \(4.9645\)  
308550.h2 308550h8 \([1, 1, 0, -38301831625, 2816047326653125]\) \(224494757451893010998773801/6152490825146276160000\) \(170304887479483783441965000000000\) \([2]\) \(1911029760\) \(4.9645\)  
308550.h3 308550h6 \([1, 1, 0, -38046279625, 2856364999037125]\) \(220031146443748723000125481/172266701724057600\) \(4768452662077706342400000000\) \([2, 2]\) \(955514880\) \(4.6179\)  
308550.h4 308550h4 \([1, 1, 0, -7516845250, 250655549321500]\) \(1696892787277117093383481/1440538624914939000\) \(39875031982702097652796875000\) \([2]\) \(637009920\) \(4.4151\)  
308550.h5 308550h5 \([1, 1, 0, -4922847250, -131526938112500]\) \(476646772170172569823801/5862293314453125000\) \(162272034475717071533203125000\) \([2]\) \(637009920\) \(4.4151\)  
308550.h6 308550h3 \([1, 1, 0, -2361927625, 45258801533125]\) \(-52643812360427830814761/1504091705903677440\) \(-41634221978162886082560000000\) \([2]\) \(477757440\) \(4.2713\)  
308550.h7 308550h2 \([1, 1, 0, -574470250, 2042158196500]\) \(757443433548897303481/373234243041000000\) \(10331362950561828140625000000\) \([2, 2]\) \(318504960\) \(4.0686\)  
308550.h8 308550h1 \([1, 1, 0, 131201750, 244811612500]\) \(9023321954633914439/6156756739584000\) \(-170422970723971416000000000\) \([2]\) \(159252480\) \(3.7220\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 308550.h have rank \(0\).

Complex multiplication

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

Modular form 308550.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - 4 q^{7} - q^{8} + q^{9} - q^{12} + 2 q^{13} + 4 q^{14} + q^{16} - q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 3 & 12 & 4 & 6 & 12 \\ 4 & 1 & 2 & 12 & 3 & 4 & 6 & 12 \\ 2 & 2 & 1 & 6 & 6 & 2 & 3 & 6 \\ 3 & 12 & 6 & 1 & 4 & 12 & 2 & 4 \\ 12 & 3 & 6 & 4 & 1 & 12 & 2 & 4 \\ 4 & 4 & 2 & 12 & 12 & 1 & 6 & 3 \\ 6 & 6 & 3 & 2 & 2 & 6 & 1 & 2 \\ 12 & 12 & 6 & 4 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.