Properties

Label 8379f
Number of curves $3$
Conductor $8379$
CM no
Rank $1$
Graph

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

Elliptic curves in class 8379f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8379.j3 8379f1 \([0, 0, 1, 294, -86]\) \(32768/19\) \(-1629556299\) \([]\) \(3024\) \(0.45709\) \(\Gamma_0(N)\)-optimal
8379.j2 8379f2 \([0, 0, 1, -4116, -108131]\) \(-89915392/6859\) \(-588269823939\) \([]\) \(9072\) \(1.0064\)  
8379.j1 8379f3 \([0, 0, 1, -339276, -76063766]\) \(-50357871050752/19\) \(-1629556299\) \([]\) \(27216\) \(1.5557\)  

Rank

sage: E.rank()
 

The elliptic curves in class 8379f have rank \(1\).

Complex multiplication

The elliptic curves in class 8379f do not have complex multiplication.

Modular form 8379.2.a.f

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

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.