Properties

 Label 206910be Number of curves $4$ Conductor $206910$ CM no Rank $1$ Graph

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("206910.cy1")

sage: E.isogeny_class()

Elliptic curves in class 206910be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
206910.cy4 206910be1 [1, -1, 1, -10913, 751457] [2] 983040 $$\Gamma_0(N)$$-optimal
206910.cy3 206910be2 [1, -1, 1, -206933, 36270281] [2, 2] 1966080
206910.cy1 206910be3 [1, -1, 1, -3310583, 2319315221] [2] 3932160
206910.cy2 206910be4 [1, -1, 1, -239603, 24077837] [2] 3932160

Rank

sage: E.rank()

The elliptic curves in class 206910be have rank $$1$$.

Modular form 206910.2.a.cy

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} - 4q^{7} + q^{8} - q^{10} + 2q^{13} - 4q^{14} + q^{16} - 2q^{17} + q^{19} + O(q^{20})$$

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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

Isogeny graph

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

The vertices are labelled with Cremona labels.