# Properties

 Label 574.g Number of curves 2 Conductor 574 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("574.g1")
sage: E.isogeny_class()

## Elliptic curves in class 574.g

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
574.g1 574i2 [1, -1, 1, -9611313, -11466507927] 1 24696
574.g2 574i1 [1, -1, 1, -19353, 958713] 7 3528 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 574.g have rank $$1$$.

## Modular form574.2.a.g

sage: E.q_eigenform(10)
$$q + q^{2} - 3q^{3} + q^{4} - q^{5} - 3q^{6} + q^{7} + q^{8} + 6q^{9} - q^{10} - 2q^{11} - 3q^{12} + q^{14} + 3q^{15} + q^{16} - 3q^{17} + 6q^{18} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 