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Properties

Label 50430.c
Number of curves $4$
Conductor $50430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 50430.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50430.c1 50430a4 \([1, 1, 0, -8822763, 10083162117]\) \(15989485458638089/615000\) \(2921314108215000\) \([2]\) \(1290240\) \(2.4584\)  
50430.c2 50430a3 \([1, 1, 0, -888443, -57140907]\) \(16327137318409/9155465640\) \(43489416164893779240\) \([2]\) \(1290240\) \(2.4584\)  
50430.c3 50430a2 \([1, 1, 0, -552243, 156884013]\) \(3921141001609/24206400\) \(114982923299342400\) \([2, 2]\) \(645120\) \(2.1119\)  
50430.c4 50430a1 \([1, 1, 0, -14323, 5298157]\) \(-68417929/2519040\) \(-11965702587248640\) \([2]\) \(322560\) \(1.7653\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 50430.c have rank \(1\).

Complex multiplication

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

Modular form 50430.2.a.c

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.