# Properties

 Label 140a Number of curves 2 Conductor 140 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("140.a1")

sage: E.isogeny_class()

## Elliptic curves in class 140a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
140.a2 140a1 [0, 1, 0, -5, -25]  12 $$\Gamma_0(N)$$-optimal
140.a1 140a2 [0, 1, 0, -805, -9065] [] 36

## Rank

sage: E.rank()

The elliptic curves in class 140a have rank $$0$$.

## Modular form140.2.a.a

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{7} - 2q^{9} + 3q^{11} - q^{13} + q^{15} - 3q^{17} + 2q^{19} + O(q^{20})$$

## 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. 