# Properties

 Label 124.a Number of curves 2 Conductor 124 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("124.a1")
sage: E.isogeny_class()

## Elliptic curves in class 124.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
124.a1 124a1 [0, 1, 0, -2, 1] 3 6 $$\Gamma_0(N)$$-optimal
124.a2 124a2 [0, 1, 0, 18, -11] 1 18

## Rank

sage: E.rank()

The elliptic curves in class 124.a have rank $$1$$.

## Modular form124.2.a.a

sage: E.q_eigenform(10)
$$q - 2q^{3} - 3q^{5} - q^{7} + q^{9} - 6q^{11} + 2q^{13} + 6q^{15} + 6q^{17} - q^{19} + O(q^{20})$$

## 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. 