Properties

Label 316050il
Number of curves $4$
Conductor $316050$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("il1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 316050il

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
316050.il3 316050il1 [1, 0, 0, -83938, 9341492] [2] 1327104 \(\Gamma_0(N)\)-optimal
316050.il2 316050il2 [1, 0, 0, -108438, 3436992] [2, 2] 2654208  
316050.il4 316050il3 [1, 0, 0, 418312, 27140742] [2] 5308416  
316050.il1 316050il4 [1, 0, 0, -1027188, -398056758] [2] 5308416  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 316050.2.a.il

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.