# Properties

 Label 59290cd Number of curves 4 Conductor 59290 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("59290.by1")

sage: E.isogeny_class()

## Elliptic curves in class 59290cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59290.by3 59290cd1 [1, 1, 0, -332147, 1433680109] [2] 3317760 $$\Gamma_0(N)$$-optimal
59290.by2 59290cd2 [1, 1, 0, -21202227, 37234215341] [2] 6635520
59290.by4 59290cd3 [1, 1, 0, 2988093, -38622359299] [2] 9953280
59290.by1 59290cd4 [1, 1, 0, -154841887, -720668834871] [2] 19906560

## Rank

sage: E.rank()

The elliptic curves in class 59290cd have rank $$0$$.

## Modular form 59290.2.a.by

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.