Properties

Label 3744.c
Number of curves $2$
Conductor $3744$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3744.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.c1 3744b2 \([0, 0, 0, -1836, -30240]\) \(8489664/13\) \(1048080384\) \([2]\) \(1536\) \(0.63042\)  
3744.c2 3744b1 \([0, 0, 0, -81, -756]\) \(-46656/169\) \(-212891328\) \([2]\) \(768\) \(0.28384\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 3744.c have rank \(0\).

Complex multiplication

The elliptic curves in class 3744.c do not have complex multiplication.

Modular form 3744.2.a.c

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + 2q^{11} + q^{13} - 4q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.