# Properties

 Label 42350.cx Number of curves 4 Conductor 42350 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("42350.cx1")

sage: E.isogeny_class()

## Elliptic curves in class 42350.cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
42350.cx1 42350cq4 [1, 1, 1, -79000963, 262577985781] [2] 9953280
42350.cx2 42350cq2 [1, 1, 1, -10817463, -13577047219] [2] 3317760
42350.cx3 42350cq1 [1, 1, 1, -169463, -522599219] [2] 1658880 $$\Gamma_0(N)$$-optimal
42350.cx4 42350cq3 [1, 1, 1, 1524537, 14076292781] [2] 4976640

## Rank

sage: E.rank()

The elliptic curves in class 42350.cx have rank $$0$$.

## Modular form 42350.2.a.cx

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{7} + q^{8} + q^{9} + 2q^{12} - 4q^{13} + q^{14} + q^{16} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.