Properties

 Label 170c Number of curves 2 Conductor 170 CM no Rank 0 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("170.e1")
sage: E.isogeny_class()

Elliptic curves in class 170c

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
170.e2 170c1 [1, 0, 0, 399, -919] 3 84 $$\Gamma_0(N)$$-optimal
170.e1 170c2 [1, 0, 0, -6641, -215575] 1 252

Rank

sage: E.rank()

The elliptic curves in class 170c have rank $$0$$.

Modular form170.2.a.e

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 2q^{7} + q^{8} - 2q^{9} - q^{10} + q^{12} - q^{13} + 2q^{14} - q^{15} + q^{16} - q^{17} - 2q^{18} - q^{19} + O(q^{20})$$

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 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.