# Properties

 Label 26640be Number of curves $6$ Conductor $26640$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("26640.p1")

sage: E.isogeny_class()

## Elliptic curves in class 26640be

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26640.p5 26640be1 [0, 0, 0, -121683, 56241682]  331776 $$\Gamma_0(N)$$-optimal
26640.p4 26640be2 [0, 0, 0, -3070803, 2066951698] [2, 2] 663552
26640.p3 26640be3 [0, 0, 0, -4222803, 375124498] [2, 2] 1327104
26640.p1 26640be4 [0, 0, 0, -49104723, 132444219922]  1327104
26640.p6 26640be5 [0, 0, 0, 16772397, 2991126418]  2654208
26640.p2 26640be6 [0, 0, 0, -43650003, -110517818222]  2654208

## Rank

sage: E.rank()

The elliptic curves in class 26640be have rank $$0$$.

## Modular form 26640.2.a.p

sage: E.q_eigenform(10)

$$q - q^{5} + 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 