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Properties

Label 16830cd
Number of curves $8$
Conductor $16830$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cd1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 16830cd have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1\)
\(5\)\(1 - T\)
\(11\)\(1 + T\)
\(17\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 2 T + 7 T^{2}\) 1.7.c
\(13\) \( 1 + 13 T^{2}\) 1.13.a
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 4 T + 23 T^{2}\) 1.23.ae
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 16830cd do not have complex multiplication.

Modular form 16830.2.a.cd

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 4 q^{7} + q^{8} - q^{10} - q^{11} + 2 q^{13} - 4 q^{14} + q^{16} + q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content 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

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 16830cd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16830.bk8 16830cd1 \([1, -1, 1, 390352, 39622547]\) \(9023321954633914439/6156756739584000\) \(-4488275663156736000\) \([2]\) \(442368\) \(2.2676\) \(\Gamma_0(N)\)-optimal
16830.bk7 16830cd2 \([1, -1, 1, -1709168, 331875731]\) \(757443433548897303481/373234243041000000\) \(272087763176889000000\) \([2, 2]\) \(884736\) \(2.6142\)  
16830.bk6 16830cd3 \([1, -1, 1, -7027223, 7346695727]\) \(-52643812360427830814761/1504091705903677440\) \(-1096482853603780853760\) \([6]\) \(1327104\) \(2.8169\)  
16830.bk5 16830cd4 \([1, -1, 1, -14646488, -21340722733]\) \(476646772170172569823801/5862293314453125000\) \(4273611826236328125000\) \([2]\) \(1769472\) \(2.9608\)  
16830.bk4 16830cd5 \([1, -1, 1, -22364168, 40683483731]\) \(1696892787277117093383481/1440538624914939000\) \(1050152657562990531000\) \([2]\) \(1769472\) \(2.9608\)  
16830.bk3 16830cd6 \([1, -1, 1, -113195543, 463573200431]\) \(220031146443748723000125481/172266701724057600\) \(125582425556837990400\) \([2, 6]\) \(2654208\) \(3.1635\)  
16830.bk2 16830cd7 \([1, -1, 1, -113955863, 457030494767]\) \(224494757451893010998773801/6152490825146276160000\) \(4485165811531635320640000\) \([6]\) \(5308416\) \(3.5101\)  
16830.bk1 16830cd8 \([1, -1, 1, -1811128343, 29667338187311]\) \(901247067798311192691198986281/552431869440\) \(402722832821760\) \([6]\) \(5308416\) \(3.5101\)