# Properties

 Label 59290br Number of curves $4$ Conductor $59290$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("59290.bc1")

sage: E.isogeny_class()

## Elliptic curves in class 59290br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
59290.bc4 59290br1 [1, -1, 0, 13711, -987827] [2] 245760 $$\Gamma_0(N)$$-optimal
59290.bc3 59290br2 [1, -1, 0, -104869, -10545375] [2, 2] 491520
59290.bc2 59290br3 [1, -1, 0, -519899, 134964143] [2] 983040
59290.bc1 59290br4 [1, -1, 0, -1587119, -769160925] [2] 983040

## Rank

sage: E.rank()

The elliptic curves in class 59290br have rank $$2$$.

## Modular form 59290.2.a.bc

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - 3q^{9} - q^{10} - 6q^{13} + q^{16} + 2q^{17} + 3q^{18} + O(q^{20})$$

## 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.