Properties

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

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Show commands: SageMath
E = EllipticCurve("jg1")
 
E.isogeny_class()
 

Elliptic curves in class 382200.jg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.jg1 382200jg3 \([0, 1, 0, -2029008, 1107553488]\) \(490757540836/2142075\) \(4032207706800000000\) \([2]\) \(10616832\) \(2.4230\)  
382200.jg2 382200jg2 \([0, 1, 0, -191508, -2296512]\) \(1650587344/950625\) \(447360322500000000\) \([2, 2]\) \(5308416\) \(2.0764\)  
382200.jg3 382200jg1 \([0, 1, 0, -136383, -19385262]\) \(9538484224/26325\) \(774277481250000\) \([2]\) \(2654208\) \(1.7298\) \(\Gamma_0(N)\)-optimal
382200.jg4 382200jg4 \([0, 1, 0, 763992, -17584512]\) \(26198797244/15234375\) \(-28676943750000000000\) \([2]\) \(10616832\) \(2.4230\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 382200.2.a.jg

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