Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3744.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.d1 3744l1 \([0, 0, 0, -26121, 1624444]\) \(42246001231552/14414517\) \(672523705152\) \([2]\) \(6144\) \(1.2411\) \(\Gamma_0(N)\)-optimal
3744.d2 3744l2 \([0, 0, 0, -22476, 2093920]\) \(-420526439488/390971529\) \(-1167434730049536\) \([2]\) \(12288\) \(1.5877\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3744.2.a.d

sage: E.q_eigenform(10)
 
\(q - 2q^{5} + 2q^{7} + 2q^{11} - q^{13} - 6q^{17} + 2q^{19} + O(q^{20})\)  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.