Properties

Label 372232.h
Number of curves $2$
Conductor $372232$
CM no
Rank $1$
Graph

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

Elliptic curves in class 372232.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
372232.h1 372232h2 \([0, 0, 0, -282931, 57924270]\) \(50668941906/1127\) \(55711826458624\) \([2]\) \(1261568\) \(1.7525\)  
372232.h2 372232h1 \([0, 0, 0, -17051, 972774]\) \(-22180932/3703\) \(-91526572039168\) \([2]\) \(630784\) \(1.4060\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 372232.h have rank \(1\).

Complex multiplication

The elliptic curves in class 372232.h do not have complex multiplication.

Modular form 372232.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.