Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("100800.op1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 100800fn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
100800.op4 100800fn1 [0, 0, 0, 33300, 3726000] [2] 589824 \(\Gamma_0(N)\)-optimal
100800.op3 100800fn2 [0, 0, 0, -254700, 40014000] [2, 2] 1179648  
100800.op2 100800fn3 [0, 0, 0, -1262700, -510354000] [2] 2359296  
100800.op1 100800fn4 [0, 0, 0, -3854700, 2912814000] [2] 2359296  

Rank

sage: E.rank()
 

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

Modular form 100800.2.a.op

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

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 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.