# Properties

 Label 284592.ka Number of curves 4 Conductor 284592 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("284592.ka1")

sage: E.isogeny_class()

## Elliptic curves in class 284592.ka

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
284592.ka1 284592ka4 [0, 1, 0, -4175992, -3286028572] [2] 6635520
284592.ka2 284592ka3 [0, 1, 0, -618592, 115415012] [2] 6635520
284592.ka3 284592ka2 [0, 1, 0, -262852, -50644420] [2, 2] 3317760
284592.ka4 284592ka1 [0, 1, 0, 3953, -2619520] [2] 1658880 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 284592.ka have rank $$0$$.

## Modular form 284592.2.a.ka

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{9} + 6q^{13} + 2q^{15} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.