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Properties

Label 430950ba
Number of curves $2$
Conductor $430950$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ba1")
 
E.isogeny_class()
 

Elliptic curves in class 430950ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
430950.ba1 430950ba1 \([1, 1, 0, -38524662530, 2910425690717940]\) \(-1834706964652838502691465/12382380341932032\) \(-42675406985986371659600179200\) \([]\) \(1154829312\) \(4.6752\) \(\Gamma_0(N)\)-optimal
430950.ba2 430950ba2 \([1, 1, 0, -21347363105, 5511987965339445]\) \(-312164053940821515126265/3627623070542340292608\) \(-12502466137540139280947106073804800\) \([]\) \(3464487936\) \(5.2245\)  

Rank

sage: E.rank()
 

The elliptic curves in class 430950ba have rank \(0\).

Complex multiplication

The elliptic curves in class 430950ba do not have complex multiplication.

Modular form 430950.2.a.ba

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