Properties

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

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

Elliptic curves in class 3744.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3744.i1 3744m2 \([0, 0, 0, -11820, 494336]\) \(61162984000/41067\) \(122625404928\) \([2]\) \(5120\) \(1.0661\)  
3744.i2 3744m1 \([0, 0, 0, -885, 4448]\) \(1643032000/767637\) \(35814871872\) \([2]\) \(2560\) \(0.71954\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 3744.2.a.i

sage: E.q_eigenform(10)
 
\(q + 2q^{7} - 4q^{11} + q^{13} + 6q^{17} + 6q^{19} + O(q^{20})\)  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.