↑

Properties

Label 18150.cc
Number of curves $4$
Conductor $18150$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("cc1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 18150.cc have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1 - T\)
\(3\)\(1 + T\)
\(5\)\(1\)
\(11\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + 2 T + 7 T^{2}\) 1.7.c
\(13\) \( 1 - 4 T + 13 T^{2}\) 1.13.ae
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 + 19 T^{2}\) 1.19.a
\(23\) \( 1 - 6 T + 23 T^{2}\) 1.23.ag
\(29\) \( 1 + 10 T + 29 T^{2}\) 1.29.k
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 18150.cc do not have complex multiplication.

Modular form 18150.2.a.cc

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 18150.cc

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18150.cc1 18150ca3 \([1, 1, 1, -30446688, 64650662781]\) \(112763292123580561/1932612\) \(53495938239562500\) \([2]\) \(960000\) \(2.7515\)  
18150.cc2 18150ca4 \([1, 1, 1, -30416438, 64785577781]\) \(-112427521449300721/466873642818\) \(-12923361524129670281250\) \([2]\) \(1920000\) \(3.0981\)  
18150.cc3 18150ca1 \([1, 1, 1, -136188, -14157219]\) \(10091699281/2737152\) \(75766120848000000\) \([2]\) \(192000\) \(1.9468\) \(\Gamma_0(N)\)-optimal
18150.cc4 18150ca2 \([1, 1, 1, 347812, -91597219]\) \(168105213359/228637728\) \(-6328838782084500000\) \([2]\) \(384000\) \(2.2934\)