Properties

Label 5184.h
Number of curves $2$
Conductor $5184$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5184.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5184.h1 5184bc2 \([0, 0, 0, -3564, 89424]\) \(-35937/4\) \(-557256278016\) \([]\) \(6912\) \(0.99122\)  
5184.h2 5184bc1 \([0, 0, 0, 276, -176]\) \(109503/64\) \(-1358954496\) \([]\) \(2304\) \(0.44191\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5184.h have rank \(0\).

Complex multiplication

The elliptic curves in class 5184.h do not have complex multiplication.

Modular form 5184.2.a.h

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.