# Properties

 Label 41070bl Number of curves 8 Conductor 41070 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("41070.bh1")

sage: E.isogeny_class()

## Elliptic curves in class 41070bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
41070.bh8 41070bl1 [1, 0, 0, 2025, 107865] [2] 103680 $$\Gamma_0(N)$$-optimal
41070.bh6 41070bl2 [1, 0, 0, -25355, 1405677] [2, 2] 207360
41070.bh7 41070bl3 [1, 0, 0, -18510, -3173628] [2] 311040
41070.bh5 41070bl4 [1, 0, 0, -93805, -9532633] [2] 414720
41070.bh4 41070bl5 [1, 0, 0, -394985, 95513475] [2] 414720
41070.bh3 41070bl6 [1, 0, 0, -456590, -118563900] [2, 2] 622080
41070.bh1 41070bl7 [1, 0, 0, -7301590, -7594672900] [2] 1244160
41070.bh2 41070bl8 [1, 0, 0, -620870, -25679988] [2] 1244160

## Rank

sage: E.rank()

The elliptic curves in class 41070bl have rank $$0$$.

## Modular form 41070.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{5} + q^{6} - 4q^{7} + q^{8} + q^{9} + q^{10} + q^{12} - 2q^{13} - 4q^{14} + q^{15} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.