Properties

Label 48552.q
Number of curves $4$
Conductor $48552$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 48552.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
48552.q1 48552c4 \([0, -1, 0, -157312, -21774020]\) \(17418812548/1753941\) \(43351932835255296\) \([2]\) \(368640\) \(1.9285\)  
48552.q2 48552c2 \([0, -1, 0, -35932, 2259220]\) \(830321872/127449\) \(787535112059136\) \([2, 2]\) \(184320\) \(1.5819\)  
48552.q3 48552c1 \([0, -1, 0, -34487, 2476548]\) \(11745974272/357\) \(137873794128\) \([4]\) \(92160\) \(1.2353\) \(\Gamma_0(N)\)-optimal
48552.q4 48552c3 \([0, -1, 0, 62328, 12360348]\) \(1083360092/3306177\) \(-81718349274842112\) \([2]\) \(368640\) \(1.9285\)  

Rank

sage: E.rank()
 

The elliptic curves in class 48552.q have rank \(1\).

Complex multiplication

The elliptic curves in class 48552.q do not have complex multiplication.

Modular form 48552.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{3} + 2 q^{5} - q^{7} + q^{9} + 4 q^{11} + 6 q^{13} - 2 q^{15} + O(q^{20})\) Copy content 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.