Properties

Label 3744i
Number of curves $2$
Conductor $3744$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 3744i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.m2 3744i1 \([0, 0, 0, -9, 28]\) \(-46656/169\) \(-292032\) \([2]\) \(256\) \(-0.26546\) \(\Gamma_0(N)\)-optimal
3744.m1 3744i2 \([0, 0, 0, -204, 1120]\) \(8489664/13\) \(1437696\) \([2]\) \(512\) \(0.081110\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3744i have rank \(1\).

Complex multiplication

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

Modular form 3744.2.a.i

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