# Properties

 Label 35739n Number of curves 2 Conductor 35739 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35739.k1")

sage: E.isogeny_class()

## Elliptic curves in class 35739n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.k2 35739n1 [0, 0, 1, -1180470, -532184666] [] 518400 $$\Gamma_0(N)$$-optimal
35739.k1 35739n2 [0, 0, 1, -97675770, -371559508025] [] 1555200

## Rank

sage: E.rank()

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

## Modular form 35739.2.a.k

sage: E.q_eigenform(10)

$$q - 2q^{4} + 2q^{7} - q^{11} + q^{13} + 4q^{16} - 3q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 