Properties

 Label 162d Number of curves 2 Conductor 162 CM no Rank 0 Graph Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162.d1")
sage: E.isogeny_class()

Elliptic curves in class 162d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
162.d2 162d1 [1, -1, 1, 4, -1] 3 12 $$\Gamma_0(N)$$-optimal
162.d1 162d2 [1, -1, 1, -56, -161] 1 36

Rank

sage: E.rank()

The elliptic curves in class 162d have rank $$0$$.

Modular form162.2.a.d

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. 