Properties

Label 840.h
Number of curves $4$
Conductor $840$
CM no
Rank $0$
Graph

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

Elliptic curves in class 840.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
840.h1 840d3 \([0, 1, 0, -202616, 34012320]\) \(898353183174324196/29899176238575\) \(30616756468300800\) \([4]\) \(7680\) \(1.9362\)  
840.h2 840d2 \([0, 1, 0, -31116, -1385280]\) \(13015144447800784/4341909875625\) \(1111528928160000\) \([2, 2]\) \(3840\) \(1.5897\)  
840.h3 840d1 \([0, 1, 0, -27991, -1811530]\) \(151591373397612544/32558203125\) \(520931250000\) \([2]\) \(1920\) \(1.2431\) \(\Gamma_0(N)\)-optimal
840.h4 840d4 \([0, 1, 0, 90384, -9452880]\) \(79743193254623804/84085819746075\) \(-86103879419980800\) \([2]\) \(7680\) \(1.9362\)  

Rank

sage: E.rank()
 

The elliptic curves in class 840.h have rank \(0\).

Complex multiplication

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

Modular form 840.2.a.h

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