Properties

Label 80850i
Number of curves 4
Conductor 80850
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("80850.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 80850i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
80850.m3 80850i1 [1, 1, 0, -613750, 160442500] [2] 1769472 \(\Gamma_0(N)\)-optimal
80850.m2 80850i2 [1, 1, 0, -2598250, -1452956000] [2, 2] 3538944  
80850.m4 80850i3 [1, 1, 0, 3465500, -7219582250] [2] 7077888  
80850.m1 80850i4 [1, 1, 0, -40414000, -98904143750] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 80850i have rank \(0\).

Modular form 80850.2.a.m

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

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.