# Properties

 Label 35739r Number of curves 3 Conductor 35739 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35739.a1")

sage: E.isogeny_class()

## Elliptic curves in class 35739r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.a3 35739r1 [0, 0, 1, -1083, 32580] [] 43200 $$\Gamma_0(N)$$-optimal
35739.a2 35739r2 [0, 0, 1, -33573, -4288590] [] 216000
35739.a1 35739r3 [0, 0, 1, -25408263, -49295874780] [] 1080000

## Rank

sage: E.rank()

The elliptic curves in class 35739r have rank $$1$$.

## Modular form 35739.2.a.a

sage: E.q_eigenform(10)

$$q - 2q^{2} + 2q^{4} - q^{5} - 2q^{7} + 2q^{10} - q^{11} - 4q^{13} + 4q^{14} - 4q^{16} + 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 