# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("35739.n1")

sage: E.isogeny_class()

## Elliptic curves in class 35739o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.n1 35739o1 [0, 0, 1, -88806, 11912368] [] 259200 $$\Gamma_0(N)$$-optimal
35739.n2 35739o2 [0, 0, 1, 625974, -68893511] [] 777600

## Rank

sage: E.rank()

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

## Modular form 35739.2.a.n

sage: E.q_eigenform(10)

$$q - 2q^{4} + 3q^{5} - 4q^{7} - q^{11} - 2q^{13} + 4q^{16} + O(q^{20})$$

## 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. 