Properties

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

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 50430.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50430.r1 50430q2 \([1, 1, 1, -1401880071, 20202310100979]\) \(64143574428979927522369/139586300156250\) \(663049476357702087656250\) \([2]\) \(22579200\) \(3.8176\)  
50430.r2 50430q1 \([1, 1, 1, -88598821, 308200413479]\) \(16192145593815022369/729711914062500\) \(3466207657696508789062500\) \([2]\) \(11289600\) \(3.4711\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 50430.2.a.r

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