Properties

Label 83790.o
Number of curves $4$
Conductor $83790$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("o1")
 
E.isogeny_class()
 

Elliptic curves in class 83790.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83790.o1 83790c4 \([1, -1, 0, -52427265, -57470785219]\) \(6882017790203934867/3366201047283200\) \(7795062170953676616614400\) \([2]\) \(17915904\) \(3.4696\)  
83790.o2 83790c2 \([1, -1, 0, -43000890, -108522798644]\) \(2768241956450868452043/2058557375000\) \(6539054848507125000\) \([2]\) \(5971968\) \(2.9203\)  
83790.o3 83790c1 \([1, -1, 0, -2669970, -1718456300]\) \(-662660286993086283/18441985352000\) \(-58581390636291096000\) \([2]\) \(2985984\) \(2.5737\) \(\Gamma_0(N)\)-optimal
83790.o4 83790c3 \([1, -1, 0, 11923455, -6878249155]\) \(80956273702840173/55667967918080\) \(-128909493151726518927360\) \([2]\) \(8957952\) \(3.1231\)  

Rank

sage: E.rank()
 

The elliptic curves in class 83790.o have rank \(0\).

Complex multiplication

The elliptic curves in class 83790.o do not have complex multiplication.

Modular form 83790.2.a.o

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 2 q^{13} + q^{16} - 6 q^{17} - q^{19} + O(q^{20})\) 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 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.