# Properties

 Label 47652.e Number of curves 2 Conductor 47652 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("47652.e1")

sage: E.isogeny_class()

## Elliptic curves in class 47652.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47652.e1 47652f2 [0, -1, 0, -4452, 55848]  78624
47652.e2 47652f1 [0, -1, 0, 963, 6030]  39312 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 47652.e have rank $$0$$.

## Modular form 47652.2.a.e

sage: E.q_eigenform(10)

$$q - q^{3} + 2q^{5} - 2q^{7} + q^{9} + q^{11} + 2q^{13} - 2q^{15} + 4q^{17} + O(q^{20})$$

## 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. 