↑

Properties

Label 29120cd
Number of curves $6$
Conductor $29120$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

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

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 29120cd have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(5\)\(1 + T\)
\(7\)\(1 - T\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - 2 T + 3 T^{2}\) 1.3.ac
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(17\) \( 1 + 6 T + 17 T^{2}\) 1.17.g
\(19\) \( 1 + 6 T + 19 T^{2}\) 1.19.g
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 - 6 T + 29 T^{2}\) 1.29.ag
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 29120cd do not have complex multiplication.

Modular form 29120.2.a.cd

Copy content sage:E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{5} - q^{7} + q^{9} - q^{13} - 2 q^{15} + 2 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 29120cd

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
29120.l6 29120cd1 \([0, 1, 0, -76545, -8145665]\) \(189208196468929/834928640\) \(218871533404160\) \([2]\) \(110592\) \(1.6041\) \(\Gamma_0(N)\)-optimal
29120.l4 29120cd2 \([0, 1, 0, -1223425, -521259777]\) \(772531501373731009/15142400\) \(3969489305600\) \([2]\) \(221184\) \(1.9507\)  
29120.l5 29120cd3 \([0, 1, 0, -424705, 100328703]\) \(32318182904349889/2067798824000\) \(542061054918656000\) \([2]\) \(331776\) \(2.1534\)  
29120.l3 29120cd4 \([0, 1, 0, -1302785, -449876225]\) \(932829715460155969/206949435875000\) \(54250552918016000000\) \([2]\) \(663552\) \(2.5000\)  
29120.l2 29120cd5 \([0, 1, 0, -33854465, 75806667775]\) \(16369358802802724130049/4976562500\) \(1304576000000000\) \([2]\) \(995328\) \(2.7027\)  
29120.l1 29120cd6 \([0, 1, 0, -33858945, 75785596543]\) \(16375858190544687071329/9025573730468750\) \(2366000000000000000000\) \([2]\) \(1990656\) \(3.0493\)