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Properties

Label 52325h
Number of curves $2$
Conductor $52325$
CM no
Rank $1$
Graph

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

Elliptic curves in class 52325h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52325.k2 52325h1 \([1, 0, 1, 424, -3327]\) \(541343375/625807\) \(-9778234375\) \([2]\) \(34560\) \(0.60330\) \(\Gamma_0(N)\)-optimal
52325.k1 52325h2 \([1, 0, 1, -2451, -32077]\) \(104154702625/32188247\) \(502941359375\) \([2]\) \(69120\) \(0.94987\)  

Rank

sage: E.rank()
 

The elliptic curves in class 52325h have rank \(1\).

Complex multiplication

The elliptic curves in class 52325h do not have complex multiplication.

Modular form 52325.2.a.h

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

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

Isogeny graph

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

The vertices are labelled with Cremona labels.