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Properties

Label 129430e
Number of curves $2$
Conductor $129430$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 129430e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
129430.a1 129430e1 \([1, 0, 1, -110979, 14287196]\) \(-12932809/70\) \(-818174019432070\) \([3]\) \(1105272\) \(1.7056\) \(\Gamma_0(N)\)-optimal
129430.a2 129430e2 \([1, 0, 1, 286556, 76143642]\) \(222641831/343000\) \(-4009052695217143000\) \([]\) \(3315816\) \(2.2549\)  

Rank

sage: E.rank()
 

The elliptic curves in class 129430e have rank \(0\).

Complex multiplication

The elliptic curves in class 129430e do not have complex multiplication.

Modular form 129430.2.a.e

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} + q^{4} - q^{5} + 2 q^{6} + q^{7} - q^{8} + q^{9} + q^{10} + 6 q^{11} - 2 q^{12} + 2 q^{13} - q^{14} + 2 q^{15} + q^{16} - 3 q^{17} - q^{18} + 5 q^{19} + O(q^{20})\) 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.