Properties

Label 38720.cc
Number of curves $2$
Conductor $38720$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cc1")
 
E.isogeny_class()
 

Elliptic curves in class 38720.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38720.cc1 38720l2 \([0, 1, 0, -45999521, 120066720959]\) \(-23178622194826561/1610510\) \(-747927425806499840\) \([]\) \(2304000\) \(2.8837\)  
38720.cc2 38720l1 \([0, 1, 0, 77279, 33404479]\) \(109902239/1100000\) \(-510844495462400000\) \([]\) \(460800\) \(2.0790\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 38720.cc have rank \(0\).

Complex multiplication

The elliptic curves in class 38720.cc do not have complex multiplication.

Modular form 38720.2.a.cc

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - 3 q^{7} - 2 q^{9} - 6 q^{13} - q^{15} + 7 q^{17} + 5 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.