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Properties

Label 9386.f
Number of curves $2$
Conductor $9386$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 9386.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9386.f1 9386f2 \([1, -1, 0, -76780, 9003842]\) \(-1064019559329/125497034\) \(-5904118527416954\) \([]\) \(91728\) \(1.7620\)  
9386.f2 9386f1 \([1, -1, 0, -970, -17548]\) \(-2146689/1664\) \(-78284345984\) \([]\) \(13104\) \(0.78906\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 9386.f have rank \(1\).

Complex multiplication

The elliptic curves in class 9386.f do not have complex multiplication.

Modular form 9386.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + q^{7} - q^{8} + 6 q^{9} + q^{10} - 2 q^{11} + 3 q^{12} + q^{13} - q^{14} - 3 q^{15} + q^{16} - 3 q^{17} - 6 q^{18} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.