Properties

 Label 16830k Number of curves 2 Conductor 16830 CM no Rank 1 Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("16830.h1")
sage: E.isogeny_class()

Elliptic curves in class 16830k

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.h2 16830k1 [1, -1, 0, 705, 3501] 3 14400 $$\Gamma_0(N)$$-optimal
16830.h1 16830k2 [1, -1, 0, -7710, -318700] 1 43200

Rank

sage: E.rank()

The elliptic curves in class 16830k have rank $$1$$.

Modular form 16830.2.a.h

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} + q^{10} + q^{11} - 4q^{13} + q^{14} + q^{16} + q^{17} + 2q^{19} + O(q^{20})$$

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.