# Properties

 Label 35739.e Number of curves 2 Conductor 35739 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35739.e1")

sage: E.isogeny_class()

## Elliptic curves in class 35739.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.e1 35739i1 [1, -1, 1, -405110, 89937244]  492480 $$\Gamma_0(N)$$-optimal
35739.e2 35739i2 [1, -1, 1, 520855, 440692786]  984960

## Rank

sage: E.rank()

The elliptic curves in class 35739.e have rank $$0$$.

## Modular form 35739.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - 4q^{7} + 3q^{8} + q^{11} - 4q^{13} + 4q^{14} - q^{16} + 4q^{17} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 