Properties

Label 83600be
Number of curves $2$
Conductor $83600$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 83600be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83600.bu1 83600be1 \([0, 1, 0, -10933, -518237]\) \(-2258403328/480491\) \(-30751424000000\) \([]\) \(186624\) \(1.3095\) \(\Gamma_0(N)\)-optimal
83600.bu2 83600be2 \([0, 1, 0, 77067, 3001763]\) \(790939860992/517504691\) \(-33120300224000000\) \([]\) \(559872\) \(1.8588\)  

Rank

sage: E.rank()
 

The elliptic curves in class 83600be have rank \(0\).

Complex multiplication

The elliptic curves in class 83600be do not have complex multiplication.

Modular form 83600.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{3} - 4 q^{7} - 2 q^{9} - q^{11} - 2 q^{13} - q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.