# Properties

 Label 430950.ix Number of curves 4 Conductor 430950 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("430950.ix1")

sage: E.isogeny_class()

## Elliptic curves in class 430950.ix

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
430950.ix1 430950ix3 [1, 0, 0, -323719588, 2237980628792] [2] 185794560 $$\Gamma_0(N)$$-optimal*
430950.ix2 430950ix4 [1, 0, 0, -271329588, -1711355021208] [2] 185794560
430950.ix3 430950ix2 [1, 0, 0, -27124588, 9069203792] [2, 2] 92897280 $$\Gamma_0(N)$$-optimal*
430950.ix4 430950ix1 [1, 0, 0, 6675412, 1126203792] [2] 46448640 $$\Gamma_0(N)$$-optimal*
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 430950.ix4.

## Rank

sage: E.rank()

The elliptic curves in class 430950.ix have rank $$0$$.

## Modular form 430950.2.a.ix

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + 4q^{7} + q^{8} + q^{9} + 4q^{11} + q^{12} + 4q^{14} + q^{16} + q^{17} + q^{18} - 8q^{19} + O(q^{20})$$

## 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.