Properties

Label 1386.g
Number of curves $4$
Conductor $1386$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1386.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1386.g1 1386g3 [1, -1, 1, -828041, -289811415] [2] 15360  
1386.g2 1386g2 [1, -1, 1, -51881, -4494999] [2, 2] 7680  
1386.g3 1386g4 [1, -1, 1, -13001, -11104599] [2] 15360  
1386.g4 1386g1 [1, -1, 1, -5801, 57705] [4] 3840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1386.g have rank \(1\).

Complex multiplication

The elliptic curves in class 1386.g do not have complex multiplication.

Modular form 1386.2.a.g

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - 2q^{5} - q^{7} + q^{8} - 2q^{10} - q^{11} + 2q^{13} - q^{14} + q^{16} - 6q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.