# Properties

 Label 201810a Number of curves $6$ Conductor $201810$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("201810.cr1")

sage: E.isogeny_class()

## Elliptic curves in class 201810a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
201810.cr6 201810a1 [1, 0, 0, 9590, 506660] [2] 921600 $$\Gamma_0(N)$$-optimal
201810.cr5 201810a2 [1, 0, 0, -67290, 5227092] [2, 2] 1843200
201810.cr2 201810a3 [1, 0, 0, -1009070, 390038400] [2, 2] 3686400
201810.cr4 201810a4 [1, 0, 0, -355590, -77169048] [2] 3686400
201810.cr1 201810a5 [1, 0, 0, -16144820, 24967469250] [2] 7372800
201810.cr3 201810a6 [1, 0, 0, -941800, 444298382] [2] 7372800

## Rank

sage: E.rank()

The elliptic curves in class 201810a have rank $$0$$.

## Modular form 201810.2.a.cr

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 4q^{11} + q^{12} + 2q^{13} + q^{14} + q^{15} + q^{16} - 2q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.