Properties

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

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Show commands: SageMath
E = EllipticCurve("s1")
 
E.isogeny_class()
 

Elliptic curves in class 100800s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.nx2 100800s1 \([0, 0, 0, -600, 9000]\) \(-55296/49\) \(-21168000000\) \([2]\) \(65536\) \(0.67842\) \(\Gamma_0(N)\)-optimal
100800.nx1 100800s2 \([0, 0, 0, -11100, 450000]\) \(21882096/7\) \(48384000000\) \([2]\) \(131072\) \(1.0250\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 100800.2.a.s

sage: E.q_eigenform(10)
 
\(q + q^{7} + 2 q^{11} + 2 q^{13} + 6 q^{17} + 4 q^{19} + O(q^{20})\) 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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.