Properties

Label 389620n
Number of curves $2$
Conductor $389620$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 389620n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
389620.n1 389620n1 \([0, 1, 0, -318570050, -2188651436875]\) \(-126142795384287538429696/9315359375\) \(-264043637915750000\) \([]\) \(38257920\) \(3.2392\) \(\Gamma_0(N)\)-optimal
389620.n2 389620n2 \([0, 1, 0, -315363550, -2234863309175]\) \(-122372013839654770813696/5297595236711512175\) \(-150160209842302131524082800\) \([]\) \(114773760\) \(3.7885\)  

Rank

sage: E.rank()
 

The elliptic curves in class 389620n have rank \(0\).

Complex multiplication

The elliptic curves in class 389620n do not have complex multiplication.

Modular form 389620.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{5} - q^{7} - 2 q^{9} + q^{13} + q^{15} - 6 q^{17} - 2 q^{19} + O(q^{20})\) 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.