Properties

Label 100800em
Number of curves $4$
Conductor $100800$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("em1")
 
E.isogeny_class()
 

Elliptic curves in class 100800em

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.mb3 100800em1 \([0, 0, 0, -6600, 205000]\) \(2725888/21\) \(244944000000\) \([2]\) \(131072\) \(1.0144\) \(\Gamma_0(N)\)-optimal
100800.mb2 100800em2 \([0, 0, 0, -11100, -110000]\) \(810448/441\) \(82301184000000\) \([2, 2]\) \(262144\) \(1.3610\)  
100800.mb4 100800em3 \([0, 0, 0, 42900, -866000]\) \(11696828/7203\) \(-5377010688000000\) \([2]\) \(524288\) \(1.7076\)  
100800.mb1 100800em4 \([0, 0, 0, -137100, -19514000]\) \(381775972/567\) \(423263232000000\) \([2]\) \(524288\) \(1.7076\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 100800.2.a.em

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

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.