Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3744.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.n1 3744a2 \([0, 0, 0, -204, -1120]\) \(8489664/13\) \(1437696\) \([2]\) \(512\) \(0.081110\)  
3744.n2 3744a1 \([0, 0, 0, -9, -28]\) \(-46656/169\) \(-292032\) \([2]\) \(256\) \(-0.26546\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3744.2.a.n

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.