Properties

Label 382200eo
Number of curves $4$
Conductor $382200$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("eo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 382200eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.eo4 382200eo1 \([0, -1, 0, -24908, -5362188]\) \(-3631696/24375\) \(-11470777500000000\) \([2]\) \(2654208\) \(1.7649\) \(\Gamma_0(N)\)-optimal
382200.eo3 382200eo2 \([0, -1, 0, -637408, -195237188]\) \(15214885924/38025\) \(71577651600000000\) \([2, 2]\) \(5308416\) \(2.1115\)  
382200.eo2 382200eo3 \([0, -1, 0, -882408, -31087188]\) \(20183398562/11567205\) \(43547843233440000000\) \([2]\) \(10616832\) \(2.4581\)  
382200.eo1 382200eo4 \([0, -1, 0, -10192408, -12521187188]\) \(31103978031362/195\) \(734129760000000\) \([2]\) \(10616832\) \(2.4581\)  

Rank

sage: E.rank()
 

The elliptic curves in class 382200eo have rank \(1\).

Complex multiplication

The elliptic curves in class 382200eo do not have complex multiplication.

Modular form 382200.2.a.eo

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 4q^{11} + q^{13} + 6q^{17} + O(q^{20})\)  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.