# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("35739.q1")

sage: E.isogeny_class()

## Elliptic curves in class 35739c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.q1 35739c1 [1, -1, 0, -45012, -3316005]  164160 $$\Gamma_0(N)$$-optimal
35739.q2 35739c2 [1, -1, 0, 57873, -16341246]  328320

## Rank

sage: E.rank()

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

## Modular form 35739.2.a.q

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 Cremona 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 Cremona labels. 