Properties

Label 479808ox
Number of curves $6$
Conductor $479808$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("479808.ox1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 479808ox

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
479808.ox5 479808ox1 [0, 0, 0, -1982567244, 33934881170288] [2] 283115520 \(\Gamma_0(N)\)-optimal
479808.ox4 479808ox2 [0, 0, 0, -2560594764, 12533759058800] [2, 2] 566231040  
479808.ox6 479808ox3 [0, 0, 0, 9876028596, 98580268761968] [2] 1132462080  
479808.ox2 479808ox4 [0, 0, 0, -24245658444, -1443184565779600] [2, 2] 1132462080  
479808.ox3 479808ox5 [0, 0, 0, -8258455884, -3317952650942608] [2] 2264924160  
479808.ox1 479808ox6 [0, 0, 0, -387193879884, -92734389270274192] [2] 2264924160  

Rank

sage: E.rank()
 

The elliptic curves in class 479808ox have rank \(0\).

Modular form 479808.2.a.ox

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + 4q^{11} - 2q^{13} + q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.