Properties

Label 297024hr
Number of curves $2$
Conductor $297024$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("hr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 297024hr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297024.hr1 297024hr1 \([0, 1, 0, -29121, -1921473]\) \(10418796526321/6390657\) \(1675272388608\) \([2]\) \(1146880\) \(1.2884\) \(\Gamma_0(N)\)-optimal
297024.hr2 297024hr2 \([0, 1, 0, -23681, -2655873]\) \(-5602762882081/8312741073\) \(-2179135195840512\) \([2]\) \(2293760\) \(1.6349\)  

Rank

sage: E.rank()
 

The elliptic curves in class 297024hr have rank \(0\).

Complex multiplication

The elliptic curves in class 297024hr do not have complex multiplication.

Modular form 297024.2.a.hr

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

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.