Properties

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

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Show commands: SageMath
E = EllipticCurve("hu1")
 
E.isogeny_class()
 

Elliptic curves in class 382200.hu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
382200.hu1 382200hu3 \([0, 1, 0, -687960408, 6945107018688]\) \(19129597231400697604/26325\) \(49553758800000000\) \([2]\) \(42467328\) \(3.3698\)  
382200.hu2 382200hu2 \([0, 1, 0, -42997908, 108504518688]\) \(18681746265374416/693005625\) \(326125675102500000000\) \([2, 2]\) \(21233664\) \(3.0232\)  
382200.hu3 382200hu4 \([0, 1, 0, -41013408, 118974740688]\) \(-4053153720264484/903687890625\) \(-1701087626306250000000000\) \([2]\) \(42467328\) \(3.3698\)  
382200.hu4 382200hu1 \([0, 1, 0, -2811783, 1529053938]\) \(83587439220736/13990184325\) \(411482798912981250000\) \([2]\) \(10616832\) \(2.6766\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 382200.2.a.hu

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} + q^{13} + 2 q^{17} + O(q^{20})\) 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.