# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("52371.c1")

sage: E.isogeny_class()

## Elliptic curves in class 52371a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
52371.c2 52371a1 [1, -1, 0, -8034, -49321]  147840 $$\Gamma_0(N)$$-optimal
52371.c1 52371a2 [1, -1, 0, -79449, 8591894]  295680

## Rank

sage: E.rank()

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

## Modular form 52371.2.a.c

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 Cremona 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 Cremona labels. 