# Properties

 Label 129430.g Number of curves $4$ Conductor $129430$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("129430.g1")

sage: E.isogeny_class()

## Elliptic curves in class 129430.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
129430.g1 129430k4 [1, -1, 0, -494954, 134145210]  1290240
129430.g2 129430k3 [1, -1, 0, -162134, -23441362]  1290240
129430.g3 129430k2 [1, -1, 0, -32704, 1849260] [2, 2] 645120
129430.g4 129430k1 [1, -1, 0, 4276, 170368]  322560 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 129430.g have rank $$0$$.

## Modular form 129430.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - 3q^{9} - q^{10} + 4q^{11} - 6q^{13} - q^{14} + q^{16} + 2q^{17} + 3q^{18} + O(q^{20})$$

## 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. 