Properties

Label 100800qb
Number of curves $2$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("qb1")
 
E.isogeny_class()
 

Elliptic curves in class 100800qb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.pz1 100800qb1 \([0, 0, 0, -10380, 394000]\) \(5177717/189\) \(4514807808000\) \([2]\) \(196608\) \(1.1978\) \(\Gamma_0(N)\)-optimal
100800.pz2 100800qb2 \([0, 0, 0, 4020, 1402000]\) \(300763/35721\) \(-853298675712000\) \([2]\) \(393216\) \(1.5444\)  

Rank

sage: E.rank()
 

The elliptic curves in class 100800qb have rank \(1\).

Complex multiplication

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

Modular form 100800.2.a.qb

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