# Properties

 Label 140790bx Number of curves $6$ Conductor $140790$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("140790.be1")

sage: E.isogeny_class()

## Elliptic curves in class 140790bx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
140790.be6 140790bx1 [1, 0, 1, 5407, -60844] [2] 442368 $$\Gamma_0(N)$$-optimal
140790.be5 140790bx2 [1, 0, 1, -23473, -511372] [2, 2] 884736
140790.be3 140790bx3 [1, 0, 1, -203973, 35083228] [2, 2] 1769472
140790.be2 140790bx4 [1, 0, 1, -305053, -64824244] [2] 1769472
140790.be1 140790bx5 [1, 0, 1, -3254423, 2259471368] [2] 3538944
140790.be4 140790bx6 [1, 0, 1, -41523, 89471488] [2] 3538944

## Rank

sage: E.rank()

The elliptic curves in class 140790bx have rank $$0$$.

## Modular form 140790.2.a.be

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - q^{13} + q^{15} + q^{16} - 6q^{17} - q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 2 & 2 \\ 4 & 2 & 4 & 1 & 8 & 8 \\ 8 & 4 & 2 & 8 & 1 & 4 \\ 8 & 4 & 2 & 8 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.