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Properties

Label 50430g
Number of curves $2$
Conductor $50430$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 50430g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50430.g2 50430g1 \([1, 1, 0, -94721863, 354791200693]\) \(7002221518249/43200\) \(579858882198583723200\) \([]\) \(5951232\) \(3.1708\) \(\Gamma_0(N)\)-optimal
50430.g1 50430g2 \([1, 1, 0, -137108278, 6654619732]\) \(21236169302809/12288000000\) \(164937637603152703488000000\) \([]\) \(17853696\) \(3.7201\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 50430.2.a.g

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.