Properties

Label 50820.m
Number of curves $4$
Conductor $50820$
CM no
Rank $0$
Graph

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

Elliptic curves in class 50820.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50820.m1 50820m4 \([0, 1, 0, -6001156, -2985452956]\) \(52702650535889104/22020583921875\) \(9986766764344524000000\) \([2]\) \(3732480\) \(2.9184\)  
50820.m2 50820m2 \([0, 1, 0, -5173516, -4530979180]\) \(33766427105425744/9823275\) \(4455047905862400\) \([2]\) \(1244160\) \(2.3691\)  
50820.m3 50820m1 \([0, 1, 0, -322021, -71484976]\) \(-130287139815424/2250652635\) \(-63794694923411760\) \([2]\) \(622080\) \(2.0225\) \(\Gamma_0(N)\)-optimal
50820.m4 50820m3 \([0, 1, 0, 1246139, -341639740]\) \(7549996227362816/6152409907875\) \(-174389911180879086000\) \([2]\) \(1866240\) \(2.5718\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50820.m have rank \(0\).

Complex multiplication

The elliptic curves in class 50820.m do not have complex multiplication.

Modular form 50820.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} - 2q^{13} - q^{15} + 6q^{17} - 8q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.