Properties

Label 10032.c
Number of curves $2$
Conductor $10032$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 10032.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
10032.c1 10032f2 \([0, -1, 0, -481013, 128565885]\) \(-3004935183806464000/2037123\) \(-8344055808\) \([]\) \(38880\) \(1.6533\)  
10032.c2 10032f1 \([0, -1, 0, -5813, 185853]\) \(-5304438784000/497763387\) \(-2038838833152\) \([]\) \(12960\) \(1.1040\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 10032.c have rank \(0\).

Complex multiplication

The elliptic curves in class 10032.c do not have complex multiplication.

Modular form 10032.2.a.c

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{7} + q^{9} - q^{11} - q^{13} + 3 q^{17} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.