Properties

 Label 162a Number of curves 2 Conductor 162 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162.a1")
sage: E.isogeny_class()

Elliptic curves in class 162a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
162.a1 162a1 [1, -1, 0, -6, 8] 3 12 $$\Gamma_0(N)$$-optimal
162.a2 162a2 [1, -1, 0, 39, -19] 1 36

Rank

sage: E.rank()

The elliptic curves in class 162a have rank $$1$$.

Modular form162.2.a.a

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} - 3q^{5} - 4q^{7} - q^{8} + 3q^{10} - q^{13} + 4q^{14} + q^{16} - 3q^{17} - 4q^{19} + O(q^{20})$$

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 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.