# Properties

 Label 52371.e Number of curves 2 Conductor 52371 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("52371.e1")

sage: E.isogeny_class()

## Elliptic curves in class 52371.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52371.e1 52371c2 [1, -1, 0, -5894217, -5463595706]  1351680
52371.e2 52371c1 [1, -1, 0, -109602, -203066825]  675840 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 52371.e have rank $$0$$.

## Modular form 52371.2.a.e

sage: E.q_eigenform(10)

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

## 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. 