# Properties

 Label 24640bt Number of curves 4 Conductor 24640 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("24640.l1")

sage: E.isogeny_class()

## Elliptic curves in class 24640bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24640.l3 24640bt1 [0, 1, 0, -3585, -1609217]  110592 $$\Gamma_0(N)$$-optimal
24640.l2 24640bt2 [0, 1, 0, -228865, -41844225]  221184
24640.l4 24640bt3 [0, 1, 0, 32255, 43326975]  331776
24640.l1 24640bt4 [0, 1, 0, -1671425, 807597823]  663552

## Rank

sage: E.rank()

The elliptic curves in class 24640bt have rank $$1$$.

## Modular form 24640.2.a.l

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. 