# Properties

 Label 24640x Number of curves 4 Conductor 24640 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("24640.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 24640x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24640.bv3 24640x1 [0, -1, 0, -3585, 1609217] [2] 110592 $$\Gamma_0(N)$$-optimal
24640.bv2 24640x2 [0, -1, 0, -228865, 41844225] [2] 221184
24640.bv4 24640x3 [0, -1, 0, 32255, -43326975] [2] 331776
24640.bv1 24640x4 [0, -1, 0, -1671425, -807597823] [2] 663552

## Rank

sage: E.rank()

The elliptic curves in class 24640x have rank $$0$$.

## Modular form 24640.2.a.bv

sage: E.q_eigenform(10)

$$q + 2q^{3} + q^{5} + q^{7} + q^{9} + q^{11} + 4q^{13} + 2q^{15} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.