Properties

Label 37200dh
Number of curves $4$
Conductor $37200$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("dh1")
 
E.isogeny_class()
 

Elliptic curves in class 37200dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37200.ea3 37200dh1 \([0, 1, 0, -97408, -11732812]\) \(1597099875769/186000\) \(11904000000000\) \([2]\) \(165888\) \(1.5353\) \(\Gamma_0(N)\)-optimal
37200.ea2 37200dh2 \([0, 1, 0, -105408, -9700812]\) \(2023804595449/540562500\) \(34596000000000000\) \([2, 2]\) \(331776\) \(1.8819\)  
37200.ea4 37200dh3 \([0, 1, 0, 266592, -62524812]\) \(32740359775271/45410156250\) \(-2906250000000000000\) \([2]\) \(663552\) \(2.2285\)  
37200.ea1 37200dh4 \([0, 1, 0, -605408, 173299188]\) \(383432500775449/18701300250\) \(1196883216000000000\) \([4]\) \(663552\) \(2.2285\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37200dh have rank \(0\).

Complex multiplication

The elliptic curves in class 37200dh do not have complex multiplication.

Modular form 37200.2.a.dh

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