↑

Properties

Label 42432.bb
Number of curves $6$
Conductor $42432$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("bb1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 42432.bb have rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 + T\)
\(13\)\(1 + T\)
\(17\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(7\) \( 1 + 7 T^{2}\) 1.7.a
\(11\) \( 1 - 4 T + 11 T^{2}\) 1.11.ae
\(19\) \( 1 + 4 T + 19 T^{2}\) 1.19.e
\(23\) \( 1 + 23 T^{2}\) 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 42432.bb do not have complex multiplication.

Modular form 42432.2.a.bb

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 42432.bb

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
42432.bb1 42432bl6 \([0, -1, 0, -1291137, 565029153]\) \(908031902324522977/161726530797\) \(42395639689248768\) \([2]\) \(524288\) \(2.1949\)  
42432.bb2 42432bl4 \([0, -1, 0, -88897, 6949345]\) \(296380748763217/92608836489\) \(24276850832572416\) \([2, 2]\) \(262144\) \(1.8483\)  
42432.bb3 42432bl2 \([0, -1, 0, -34817, -2406495]\) \(17806161424897/668584449\) \(175265401798656\) \([2, 2]\) \(131072\) \(1.5017\)  
42432.bb4 42432bl1 \([0, -1, 0, -34497, -2454687]\) \(17319700013617/25857\) \(6778257408\) \([2]\) \(65536\) \(1.1552\) \(\Gamma_0(N)\)-optimal
42432.bb5 42432bl3 \([0, -1, 0, 14143, -8683167]\) \(1193377118543/124806800313\) \(-32717353861251072\) \([2]\) \(262144\) \(1.8483\)  
42432.bb6 42432bl5 \([0, -1, 0, 248063, 46778017]\) \(6439735268725823/7345472585373\) \(-1925571565420019712\) \([2]\) \(524288\) \(2.1949\)