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Properties

Label 38291.d
Number of curves $3$
Conductor $38291$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 38291.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38291.d1 38291c3 \([0, -1, 1, -27222580, 54678189475]\) \(-52893159101157376/11\) \(-463985870051\) \([]\) \(1036750\) \(2.5355\)  
38291.d2 38291c2 \([0, -1, 1, -35970, 4768035]\) \(-122023936/161051\) \(-6793217123416691\) \([]\) \(207350\) \(1.7308\)  
38291.d3 38291c1 \([0, -1, 1, -1160, -35745]\) \(-4096/11\) \(-463985870051\) \([]\) \(41470\) \(0.92604\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38291.d have rank \(0\).

Complex multiplication

The elliptic curves in class 38291.d do not have complex multiplication.

Modular form 38291.2.a.d

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{9} + 2 q^{10} - q^{11} - 2 q^{12} - 4 q^{13} - 4 q^{14} - q^{15} - 4 q^{16} - 2 q^{17} - 4 q^{18} + O(q^{20})\) 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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.