Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("iv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800.iv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.iv1 100800ft4 [0, 0, 0, -5378700, -4801354000] [2] 2359296  
100800.iv2 100800ft2 [0, 0, 0, -338700, -73834000] [2, 2] 1179648  
100800.iv3 100800ft1 [0, 0, 0, -50700, 2774000] [2] 589824 \(\Gamma_0(N)\)-optimal
100800.iv4 100800ft3 [0, 0, 0, 93300, -249226000] [2] 2359296  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 100800.2.a.iv

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

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 LMFDB 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 LMFDB labels.