Properties

Label 1386.h
Number of curves $2$
Conductor $1386$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1386.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1386.h1 1386f1 \([1, -1, 1, -26, 25]\) \(69426531/34496\) \(931392\) \([2]\) \(192\) \(-0.16167\) \(\Gamma_0(N)\)-optimal
1386.h2 1386f2 \([1, -1, 1, 94, 121]\) \(3436115229/2324168\) \(-62752536\) \([2]\) \(384\) \(0.18491\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1386.2.a.h

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