# Properties

 Label 40656.ce Number of curves 6 Conductor 40656 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("40656.ce1")

sage: E.isogeny_class()

## Elliptic curves in class 40656.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
40656.ce1 40656dk6 [0, 1, 0, -8748824, -9963217068] [2] 1228800
40656.ce2 40656dk4 [0, 1, 0, -549864, -153981324] [2, 2] 614400
40656.ce3 40656dk2 [0, 1, 0, -75544, 4441556] [2, 2] 307200
40656.ce4 40656dk1 [0, 1, 0, -65864, 6482100] [2] 153600 $$\Gamma_0(N)$$-optimal
40656.ce5 40656dk5 [0, 1, 0, 59976, -476220780] [2] 1228800
40656.ce6 40656dk3 [0, 1, 0, 243896, 32424500] [2] 614400

## Rank

sage: E.rank()

The elliptic curves in class 40656.ce have rank $$1$$.

## Modular form 40656.2.a.ce

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} + q^{7} + q^{9} - 6q^{13} - 2q^{15} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.