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Properties

Label 229242.h
Number of curves $2$
Conductor $229242$
CM no
Rank $0$
Graph

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

Elliptic curves in class 229242.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229242.h1 229242b1 \([1, 0, 0, -20834021, 36600720897]\) \(-1000099030268818209411019729/6608026478667055104\) \(-6608026478667055104\) \([7]\) \(10536960\) \(2.7940\) \(\Gamma_0(N)\)-optimal
229242.h2 229242b2 \([1, 0, 0, 148038319, -450912048483]\) \(358794805479514151598884837231/295475652831033359840216724\) \(-295475652831033359840216724\) \([]\) \(73758720\) \(3.7670\)  

Rank

sage: E.rank()
 

The elliptic curves in class 229242.h have rank \(0\).

Complex multiplication

The elliptic curves in class 229242.h do not have complex multiplication.

Modular form 229242.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{7} + q^{8} + q^{9} - q^{10} - 2 q^{11} + q^{12} + q^{13} + q^{14} - q^{15} + q^{16} + 4 q^{17} + q^{18} - q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.