Properties

Label 133848z
Number of curves 4
Conductor 133848
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("133848.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 133848z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
133848.g4 133848z1 [0, 0, 0, 1014, -340535] [2] 368640 \(\Gamma_0(N)\)-optimal
133848.g3 133848z2 [0, 0, 0, -67431, -6569030] [2, 2] 737280  
133848.g2 133848z3 [0, 0, 0, -158691, 15023086] [2] 1474560  
133848.g1 133848z4 [0, 0, 0, -1071291, -426784826] [2] 1474560  

Rank

sage: E.rank()
 

The elliptic curves in class 133848z have rank \(2\).

Modular form 133848.2.a.g

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 4q^{7} - q^{11} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.