# Properties

 Label 627.a Number of curves 2 Conductor 627 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("627.a1")

sage: E.isogeny_class()

## Elliptic curves in class 627.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
627.a1 627b2 [0, 1, 1, -30063, -2016358] [] 540
627.a2 627b1 [0, 1, 1, -363, -2995]  180 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 627.a have rank $$0$$.

## Modular form627.2.a.a

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} + 2q^{7} + q^{9} + q^{11} - 2q^{12} - q^{13} + 4q^{16} + 3q^{17} + q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 