Properties

Label 840h
Number of curves $4$
Conductor $840$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 840h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
840.g3 840h1 \([0, 1, 0, -71, -246]\) \(2508888064/118125\) \(1890000\) \([2]\) \(192\) \(-0.034864\) \(\Gamma_0(N)\)-optimal
840.g2 840h2 \([0, 1, 0, -196, 704]\) \(3269383504/893025\) \(228614400\) \([2, 2]\) \(384\) \(0.31171\)  
840.g1 840h3 \([0, 1, 0, -2896, 59024]\) \(2624033547076/324135\) \(331914240\) \([2]\) \(768\) \(0.65828\)  
840.g4 840h4 \([0, 1, 0, 504, 5184]\) \(13799183324/18600435\) \(-19046845440\) \([2]\) \(768\) \(0.65828\)  

Rank

sage: E.rank()
 

The elliptic curves in class 840h have rank \(1\).

Complex multiplication

The elliptic curves in class 840h do not have complex multiplication.

Modular form 840.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} - q^{7} + q^{9} - 4 q^{11} - 6 q^{13} - q^{15} - 2 q^{17} - 8 q^{19} + O(q^{20})\) 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 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.