# Properties

 Label 20230r Number of curves $4$ Conductor $20230$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("20230.n1")

sage: E.isogeny_class()

## Elliptic curves in class 20230r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20230.n4 20230r1 [1, -1, 1, 668, -10761]  20480 $$\Gamma_0(N)$$-optimal
20230.n3 20230r2 [1, -1, 1, -5112, -112489] [2, 2] 40960
20230.n1 20230r3 [1, -1, 1, -77362, -8262289]  81920
20230.n2 20230r4 [1, -1, 1, -25342, 1457359]  81920

## Rank

sage: E.rank()

The elliptic curves in class 20230r have rank $$0$$.

## Modular form 20230.2.a.n

sage: E.q_eigenform(10)

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

## 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. 