# Properties

 Label 574.i Number of curves 2 Conductor 574 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("574.i1")
sage: E.isogeny_class()

## Elliptic curves in class 574.i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
574.i1 574j2 [1, 1, 1, -15785, -769911] 1 600
574.i2 574j1 [1, 1, 1, -175, 789] 5 120 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 574.i have rank $$0$$.

## Modular form574.2.a.i

sage: E.q_eigenform(10)
$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} - 2q^{9} + q^{10} + 2q^{11} - q^{12} + 4q^{13} + q^{14} - q^{15} + q^{16} + 3q^{17} - 2q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.