# Properties

 Label 47040.gg Number of curves 4 Conductor 47040 CM no Rank 0 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("47040.gg1")

sage: E.isogeny_class()

## Elliptic curves in class 47040.gg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47040.gg1 47040df4 [0, 1, 0, -352865, 80555775] [2] 393216
47040.gg2 47040df2 [0, 1, 0, -23585, 1067583] [2, 2] 196608
47040.gg3 47040df1 [0, 1, 0, -7905, -258945] [2] 98304 $$\Gamma_0(N)$$-optimal
47040.gg4 47040df3 [0, 1, 0, 54815, 6728063] [2] 393216

## Rank

sage: E.rank()

The elliptic curves in class 47040.gg have rank $$0$$.

## Modular form 47040.2.a.gg

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{9} - 6q^{13} + q^{15} - 2q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.