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Properties

Label 3762l
Number of curves $2$
Conductor $3762$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 3762l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3762.q2 3762l1 \([1, -1, 1, 34, -187]\) \(165469149/603592\) \(-16296984\) \([3]\) \(1440\) \(0.066763\) \(\Gamma_0(N)\)-optimal
3762.q1 3762l2 \([1, -1, 1, -1676, -26027]\) \(-26436959739/50578\) \(-995526774\) \([]\) \(4320\) \(0.61607\)  

Rank

sage: E.rank()
 

The elliptic curves in class 3762l have rank \(1\).

Complex multiplication

The elliptic curves in class 3762l do not have complex multiplication.

Modular form 3762.2.a.l

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 3 q^{5} - 4 q^{7} + q^{8} + 3 q^{10} - q^{11} - 4 q^{13} - 4 q^{14} + q^{16} - 3 q^{17} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.