# Properties

 Label 26010bm Number of curves $8$ Conductor $26010$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("26010.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 26010bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
26010.bl8 26010bm1 [1, -1, 1, 3847, -282999] [2] 73728 $$\Gamma_0(N)$$-optimal
26010.bl6 26010bm2 [1, -1, 1, -48173, -3674703] [2, 2] 147456
26010.bl7 26010bm3 [1, -1, 1, -35168, 8315907] [2] 221184
26010.bl5 26010bm4 [1, -1, 1, -178223, 24988317] [2] 294912
26010.bl4 26010bm5 [1, -1, 1, -750443, -250031019] [2] 294912
26010.bl3 26010bm6 [1, -1, 1, -867488, 310614531] [2, 2] 442368
26010.bl1 26010bm7 [1, -1, 1, -13872488, 19890942531] [2] 884736
26010.bl2 26010bm8 [1, -1, 1, -1179608, 67410627] [2] 884736

## Rank

sage: E.rank()

The elliptic curves in class 26010bm have rank $$1$$.

## Modular form 26010.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 4q^{7} + q^{8} - q^{10} + 2q^{13} + 4q^{14} + q^{16} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.