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Properties

Label 50430.h
Number of curves $2$
Conductor $50430$
CM no
Rank $0$
Graph

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

Elliptic curves in class 50430.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50430.h1 50430h1 \([1, 1, 0, -88287, -3301839]\) \(16022066761/8302500\) \(39437740460902500\) \([2]\) \(430080\) \(1.8764\) \(\Gamma_0(N)\)-optimal
50430.h2 50430h2 \([1, 1, 0, 331963, -25238889]\) \(851701809239/551452050\) \(-2619454721413144050\) \([2]\) \(860160\) \(2.2230\)  

Rank

sage: E.rank()
 

The elliptic curves in class 50430.h have rank \(0\).

Complex multiplication

The elliptic curves in class 50430.h do not have complex multiplication.

Modular form 50430.2.a.h

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