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Properties

Label 95550.iw
Number of curves $6$
Conductor $95550$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("iw1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 95550.iw 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 \(\mathbb{F}_p\)
\(11\) \( 1 + 6 T + 11 T^{2}\) 1.11.g
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 + 2 T + 19 T^{2}\) 1.19.c
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 29 T^{2}\) 1.29.a
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

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

Modular form 95550.2.a.iw

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 6 q^{11} + q^{12} + q^{13} + q^{16} + 6 q^{17} + q^{18} - 2 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 95550.iw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
95550.iw1 95550kg5 \([1, 0, 0, -1044035063, 12983980984617]\) \(68463752473882049153689/1817088000000000\) \(3340290408000000000000000\) \([2]\) \(53747712\) \(3.8109\)  
95550.iw2 95550kg6 \([1, 0, 0, -1003267063, 14044560504617]\) \(-60752633741424905775769/11197265625000000000\) \(-20583548492431640625000000000\) \([2]\) \(107495424\) \(4.1575\)  
95550.iw3 95550kg3 \([1, 0, 0, -22366688, -11662483008]\) \(673163386034885929/357608625192000\) \(657379642893962625000000\) \([2]\) \(17915904\) \(3.2616\)  
95550.iw4 95550kg1 \([1, 0, 0, -17570813, -28350308883]\) \(326355561310674169/465699780\) \(856079897144062500\) \([2]\) \(5971968\) \(2.7123\) \(\Gamma_0(N)\)-optimal
95550.iw5 95550kg2 \([1, 0, 0, -17411563, -28889370133]\) \(-317562142497484249/12339342574650\) \(-22682989290078091406250\) \([2]\) \(11943936\) \(3.0589\)  
95550.iw6 95550kg4 \([1, 0, 0, 85286312, -91218050008]\) \(37321015309599759191/23553520979625000\) \(-43297627964560962890625000\) \([2]\) \(35831808\) \(3.6082\)