Properties

Label 19320.bb
Number of curves $4$
Conductor $19320$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

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

Elliptic curves in class 19320.bb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19320.bb1 19320l3 \([0, 1, 0, -185480, -30808272]\) \(344577854816148242/2716875\) \(5564160000\) \([2]\) \(61440\) \(1.4609\)  
19320.bb2 19320l2 \([0, 1, 0, -11600, -483600]\) \(168591300897604/472410225\) \(483748070400\) \([2, 2]\) \(30720\) \(1.1143\)  
19320.bb3 19320l4 \([0, 1, 0, -7000, -866320]\) \(-18524646126002/146738831715\) \(-300521127352320\) \([2]\) \(61440\) \(1.4609\)  
19320.bb4 19320l1 \([0, 1, 0, -1020, -1152]\) \(458891455696/264449745\) \(67699134720\) \([2]\) \(15360\) \(0.76776\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19320.bb have rank \(0\).

Complex multiplication

The elliptic curves in class 19320.bb do not have complex multiplication.

Modular form 19320.2.a.bb

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} + q^{7} + q^{9} - 4 q^{11} + 2 q^{13} + q^{15} - 2 q^{17} - 4 q^{19} + O(q^{20})\)  Toggle raw display

Isogeny matrix

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.