# Properties

 Label 36.a Number of curves $4$ Conductor $36$ CM -3 Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("36.a1")

sage: E.isogeny_class()

## Elliptic curves in class 36.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
36.a1 36a4 [0, 0, 0, -135, -594]  6
36.a2 36a2 [0, 0, 0, -15, 22]  2
36.a3 36a3 [0, 0, 0, 0, -27]  3
36.a4 36a1 [0, 0, 0, 0, 1]  1 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 36.a have rank $$0$$.

## Modular form36.2.a.a

sage: E.q_eigenform(10)

$$q - 4q^{7} + 2q^{13} + 8q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 