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Properties

Label 18150.cf
Number of curves $6$
Conductor $18150$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("cf1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 18150.cf 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 \(\mathbb{F}_p\)
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(13\) \( 1 + 2 T + 13 T^{2}\) 1.13.c
\(17\) \( 1 - 2 T + 17 T^{2}\) 1.17.ac
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 - 2 T + 29 T^{2}\) 1.29.ac
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 18150.2.a.cf

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 18150.cf

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18150.cf1 18150bw5 \([1, 1, 1, -11752188, 15501461031]\) \(6484907238722641/283593750\) \(7850056677246093750\) \([2]\) \(737280\) \(2.7038\)  
18150.cf2 18150bw3 \([1, 1, 1, -3554438, -2580778969]\) \(179415687049201/1443420\) \(39954790290937500\) \([2]\) \(368640\) \(2.3572\)  
18150.cf3 18150bw4 \([1, 1, 1, -771438, 216257031]\) \(1834216913521/329422500\) \(9118625836289062500\) \([2, 2]\) \(368640\) \(2.3572\)  
18150.cf4 18150bw2 \([1, 1, 1, -226938, -38568969]\) \(46694890801/3920400\) \(108519183506250000\) \([2, 2]\) \(184320\) \(2.0106\)  
18150.cf5 18150bw1 \([1, 1, 1, 15062, -2752969]\) \(13651919/126720\) \(-3507690780000000\) \([4]\) \(92160\) \(1.6640\) \(\Gamma_0(N)\)-optimal
18150.cf6 18150bw6 \([1, 1, 1, 1497312, 1250807031]\) \(13411719834479/32153832150\) \(-890038672460721093750\) \([2]\) \(737280\) \(2.7038\)