# Properties

 Label 35739q Number of curves 4 Conductor 35739 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("35739.t1")

sage: E.isogeny_class()

## Elliptic curves in class 35739q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
35739.t3 35739q1 [1, -1, 0, -21186, -1171665] [2] 86400 $$\Gamma_0(N)$$-optimal
35739.t2 35739q2 [1, -1, 0, -37431, 884952] [2, 2] 172800
35739.t4 35739q3 [1, -1, 0, 141264, 6781887] [2] 345600
35739.t1 35739q4 [1, -1, 0, -476046, 126416565] [2] 345600

## Rank

sage: E.rank()

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

## Modular form 35739.2.a.t

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} + 2q^{5} + 4q^{7} - 3q^{8} + 2q^{10} - q^{11} + 2q^{13} + 4q^{14} - q^{16} + 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.