# Properties

 Label 142.e Number of curves 2 Conductor 142 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("142.e1")
sage: E.isogeny_class()

## Elliptic curves in class 142.e

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
142.e1 142d2 [1, 0, 0, -58, -170] 1 12
142.e2 142d1 [1, 0, 0, -8, 8] 3 4 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 142.e have rank $$0$$.

## Modular form142.2.a.e

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.