Properties

Label 38808.p
Number of curves 4
Conductor 38808
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38808.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38808.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38808.p1 38808cn4 [0, 0, 0, -310611, 66630494] [2] 221184  
38808.p2 38808cn3 [0, 0, 0, -46011, -2345434] [2] 221184  
38808.p3 38808cn2 [0, 0, 0, -19551, 1025570] [2, 2] 110592  
38808.p4 38808cn1 [0, 0, 0, 294, 53165] [2] 55296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38808.p have rank \(1\).

Modular form 38808.2.a.p

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{11} - 6q^{13} + 6q^{17} + 8q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.