Properties

Label 316050n
Number of curves $2$
Conductor $316050$
CM no
Rank $1$
Graph

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

Elliptic curves in class 316050n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
316050.n2 316050n1 [1, 1, 0, -12563625, 17768917125] [2] 34836480 \(\Gamma_0(N)\)-optimal
316050.n1 316050n2 [1, 1, 0, -203075625, 1113784453125] [2] 69672960  

Rank

sage: E.rank()
 

The elliptic curves in class 316050n have rank \(1\).

Complex multiplication

The elliptic curves in class 316050n do not have complex multiplication.

Modular form 316050.2.a.n

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} - 4q^{11} - q^{12} + 4q^{13} + q^{16} + 4q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.