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Properties

Label 95550ke
Number of curves $4$
Conductor $95550$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("ke1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 95550ke have rank \(1\).

L-function data

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

Complex multiplication

The elliptic curves in class 95550ke do not have complex multiplication.

Modular form 95550.2.a.ke

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 6 q^{11} + q^{12} + q^{13} + q^{16} + q^{18} - 8 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.

Elliptic curves in class 95550ke

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.li3 95550ke1 \([1, 0, 0, -929188, 154724492]\) \(48264326765929/22299191460\) \(40991837126211562500\) \([2]\) \(3981312\) \(2.4580\) \(\Gamma_0(N)\)-optimal
95550.li4 95550ke2 \([1, 0, 0, 3272562, 1167346242]\) \(2108526614950391/1540302022350\) \(-2831484259803986718750\) \([2]\) \(7962624\) \(2.8046\)  
95550.li1 95550ke3 \([1, 0, 0, -63055063, 192715224617]\) \(15082569606665230489/7751016000\) \(14248426271625000000\) \([2]\) \(11943936\) \(3.0073\)  
95550.li2 95550ke4 \([1, 0, 0, -62712063, 194915569617]\) \(-14837772556740428569/342100087875000\) \(-628870831850091796875000\) \([2]\) \(23887872\) \(3.3539\)