# Properties

 Label 52371.b Number of curves 2 Conductor 52371 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("52371.b1")

sage: E.isogeny_class()

## Elliptic curves in class 52371.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52371.b1 52371b2 [1, -1, 1, -8828, -315276]  98560
52371.b2 52371b1 [1, -1, 1, -893, 2124]  49280 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 52371.b have rank $$1$$.

## Modular form 52371.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} + 4q^{5} + 2q^{7} + 3q^{8} - 4q^{10} + q^{11} - 2q^{13} - 2q^{14} - q^{16} - 2q^{17} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 