Properties

Label 100800na
Number of curves $4$
Conductor $100800$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("na1")
 
E.isogeny_class()
 

Elliptic curves in class 100800na

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100800.mw4 100800na1 \([0, 0, 0, -6600, 1339000]\) \(-2725888/64827\) \(-756142128000000\) \([2]\) \(393216\) \(1.5356\) \(\Gamma_0(N)\)-optimal
100800.mw3 100800na2 \([0, 0, 0, -227100, 41470000]\) \(6940769488/35721\) \(6666395904000000\) \([2, 2]\) \(786432\) \(1.8822\)  
100800.mw2 100800na3 \([0, 0, 0, -353100, -9686000]\) \(6522128932/3720087\) \(2777030065152000000\) \([2]\) \(1572864\) \(2.2288\)  
100800.mw1 100800na4 \([0, 0, 0, -3629100, 2661010000]\) \(7080974546692/189\) \(141087744000000\) \([2]\) \(1572864\) \(2.2288\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 100800.2.a.na

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