# Properties

 Label 271040.bk Number of curves 4 Conductor 271040 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("271040.bk1")

sage: E.isogeny_class()

## Elliptic curves in class 271040.bk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
271040.bk1 271040bk4 [0, 1, 0, -202242465, -1075721672225] [2] 79626240
271040.bk2 271040bk2 [0, 1, 0, -27692705, 55583892703] [2] 26542080
271040.bk3 271040bk1 [0, 1, 0, -433825, 2140132575] [2] 13271040 $$\Gamma_0(N)$$-optimal
271040.bk4 271040bk3 [0, 1, 0, 3902815, -57652592417] [2] 39813120

## Rank

sage: E.rank()

The elliptic curves in class 271040.bk have rank $$1$$.

## Modular form 271040.2.a.bk

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.