Properties

Label 41070bl
Number of curves $8$
Conductor $41070$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bl1")
 
E.isogeny_class()
 

Elliptic curves in class 41070bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.bh8 41070bl1 \([1, 0, 0, 2025, 107865]\) \(357911/2160\) \(-5541969043440\) \([2]\) \(103680\) \(1.1272\) \(\Gamma_0(N)\)-optimal
41070.bh6 41070bl2 \([1, 0, 0, -25355, 1405677]\) \(702595369/72900\) \(187041455216100\) \([2, 2]\) \(207360\) \(1.4737\)  
41070.bh7 41070bl3 \([1, 0, 0, -18510, -3173628]\) \(-273359449/1536000\) \(-3940955764224000\) \([2]\) \(311040\) \(1.6765\)  
41070.bh5 41070bl4 \([1, 0, 0, -93805, -9532633]\) \(35578826569/5314410\) \(13635322085253690\) \([2]\) \(414720\) \(1.8203\)  
41070.bh4 41070bl5 \([1, 0, 0, -394985, 95513475]\) \(2656166199049/33750\) \(86593266303750\) \([2]\) \(414720\) \(1.8203\)  
41070.bh3 41070bl6 \([1, 0, 0, -456590, -118563900]\) \(4102915888729/9000000\) \(23091537681000000\) \([2, 2]\) \(622080\) \(2.0231\)  
41070.bh1 41070bl7 \([1, 0, 0, -7301590, -7594672900]\) \(16778985534208729/81000\) \(207823839129000\) \([2]\) \(1244160\) \(2.3696\)  
41070.bh2 41070bl8 \([1, 0, 0, -620870, -25679988]\) \(10316097499609/5859375000\) \(15033553177734375000\) \([2]\) \(1244160\) \(2.3696\)  

Rank

sage: E.rank()
 

The elliptic curves in class 41070bl have rank \(0\).

Complex multiplication

The elliptic curves in class 41070bl do not have complex multiplication.

Modular form 41070.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4 q^{7} + q^{8} + q^{9} + q^{10} + q^{12} - 2 q^{13} - 4 q^{14} + q^{15} + q^{16} - 6 q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.