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Properties

Label 88200.hq
Number of curves $6$
Conductor $88200$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("hq1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 88200.hq have rank \(0\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1\)
\(5\)\(1\)
\(7\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(13\) \( 1 - 6 T + 13 T^{2}\) 1.13.ag
\(17\) \( 1 - 6 T + 17 T^{2}\) 1.17.ag
\(19\) \( 1 - 4 T + 19 T^{2}\) 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 88200.hq do not have complex multiplication.

Modular form 88200.2.a.hq

Copy content sage:E.q_eigenform(10)
 
\(q + 4 q^{11} + 6 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 88200.hq

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
88200.hq1 88200gv6 \([0, 0, 0, -35283675, -80669398250]\) \(1770025017602/75\) \(205838690400000000\) \([2]\) \(4718592\) \(2.8070\)  
88200.hq2 88200gv4 \([0, 0, 0, -2208675, -1256323250]\) \(868327204/5625\) \(7718950890000000000\) \([2, 2]\) \(2359296\) \(2.4604\)  
88200.hq3 88200gv5 \([0, 0, 0, -885675, -2747344250]\) \(-27995042/1171875\) \(-3216229537500000000000\) \([2]\) \(4718592\) \(2.8070\)  
88200.hq4 88200gv2 \([0, 0, 0, -224175, 7803250]\) \(3631696/2025\) \(694705580100000000\) \([2, 2]\) \(1179648\) \(2.1138\)  
88200.hq5 88200gv1 \([0, 0, 0, -169050, 26711125]\) \(24918016/45\) \(964868861250000\) \([2]\) \(589824\) \(1.7673\) \(\Gamma_0(N)\)-optimal
88200.hq6 88200gv3 \([0, 0, 0, 878325, 61825750]\) \(54607676/32805\) \(-45016921590480000000\) \([2]\) \(2359296\) \(2.4604\)