Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("il1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800il

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.py2 100800il1 \([0, 0, 0, 14100, 52400]\) \(2595575/1512\) \(-180592312320000\) \([]\) \(331776\) \(1.4250\) \(\Gamma_0(N)\)-optimal
100800.py1 100800il2 \([0, 0, 0, -201900, 36945200]\) \(-7620530425/526848\) \(-62926387937280000\) \([]\) \(995328\) \(1.9743\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 100800.2.a.il

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 Cremona 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 Cremona labels.