Properties

Label 100800.hx
Number of curves $2$
Conductor $100800$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.hx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.hx1 100800eh2 \([0, 0, 0, -5047500, 4618150000]\) \(-7620530425/526848\) \(-983224811520000000000\) \([]\) \(4976640\) \(2.7791\)  
100800.hx2 100800eh1 \([0, 0, 0, 352500, 6550000]\) \(2595575/1512\) \(-2821754880000000000\) \([]\) \(1658880\) \(2.2298\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 100800.hx have rank \(0\).

Complex multiplication

The elliptic curves in class 100800.hx do not have complex multiplication.

Modular form 100800.2.a.hx

sage: E.q_eigenform(10)
 
\(q - q^{7} + 6q^{11} - q^{13} + 3q^{17} + 4q^{19} + O(q^{20})\)  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.