↑

Properties

Label 9555.d
Number of curves $6$
Conductor $9555$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("d1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 9555.d have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1 - T\)
\(5\)\(1 + T\)
\(7\)\(1\)
\(13\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + T + 2 T^{2}\) 1.2.b
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 23 T^{2}\) 1.23.a
\(29\) \( 1 + 2 T + 29 T^{2}\) 1.29.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 9555.d do not have complex multiplication.

Modular form 9555.2.a.d

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} - q^{4} - q^{5} - q^{6} + 3 q^{8} + q^{9} + q^{10} + 4 q^{11} - q^{12} - q^{13} - q^{15} - q^{16} - 2 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) 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 9555.d

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9555.d1 9555q5 \([1, 0, 0, -6697076, 6669786885]\) \(282352188585428161201/20813369346315\) \(2448672090224613435\) \([2]\) \(294912\) \(2.5788\)  
9555.d2 9555q3 \([1, 0, 0, -2295651, -1338959070]\) \(11372424889583066401/50586128775\) \(5951407464249975\) \([2]\) \(147456\) \(2.2322\)  
9555.d3 9555q4 \([1, 0, 0, -445901, 89800080]\) \(83339496416030401/18593645841225\) \(2187523839574280025\) \([2, 2]\) \(147456\) \(2.2322\)  
9555.d4 9555q2 \([1, 0, 0, -145776, -20225745]\) \(2912015927948401/184878500625\) \(21750770720030625\) \([2, 2]\) \(73728\) \(1.8857\)  
9555.d5 9555q1 \([1, 0, 0, 7349, -1330120]\) \(373092501599/6718359375\) \(-790408262109375\) \([2]\) \(36864\) \(1.5391\) \(\Gamma_0(N)\)-optimal
9555.d6 9555q6 \([1, 0, 0, 1003274, 552666575]\) \(949279533867428399/1670570708285115\) \(-196540973259035494635\) \([2]\) \(294912\) \(2.5788\)