Properties

Label 38808cd
Number of curves 4
Conductor 38808
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38808.ca1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38808cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38808.ca3 38808cd1 [0, 0, 0, -5439, -148862] [2] 49152 \(\Gamma_0(N)\)-optimal
38808.ca2 38808cd2 [0, 0, 0, -14259, 456190] [2, 2] 98304  
38808.ca4 38808cd3 [0, 0, 0, 38661, 3049270] [2] 196608  
38808.ca1 38808cd4 [0, 0, 0, -208299, 36586438] [2] 196608  

Rank

sage: E.rank()
 

The elliptic curves in class 38808cd have rank \(0\).

Modular form 38808.2.a.ca

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{11} - 2q^{13} + 6q^{17} + O(q^{20}) \)

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.