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Properties

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

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

Elliptic curves in class 50430c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
50430.d2 50430c1 \([1, 1, 0, 204207, 1016816373]\) \(198257271191/94128829920\) \(-447121754203359690720\) \([]\) \(3024000\) \(2.6415\) \(\Gamma_0(N)\)-optimal
50430.d1 50430c2 \([1, 1, 0, -1838208, -27481817088]\) \(-144612187806169/68599001088000\) \(-325852405996472414208000\) \([]\) \(9072000\) \(3.1908\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 50430.2.a.c

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