# Properties

 Label 45486.bl Number of curves $6$ Conductor $45486$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("45486.bl1")

sage: E.isogeny_class()

## Elliptic curves in class 45486.bl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
45486.bl1 45486bh4 [1, -1, 1, -4366724, 3513311435] [2] 884736
45486.bl2 45486bh6 [1, -1, 1, -2969654, -1950077005] [2] 1769472
45486.bl3 45486bh3 [1, -1, 1, -337964, 26848523] [2, 2] 884736
45486.bl4 45486bh2 [1, -1, 1, -272984, 54919883] [2, 2] 442368
45486.bl5 45486bh1 [1, -1, 1, -13064, 1272395] [2] 221184 $$\Gamma_0(N)$$-optimal
45486.bl6 45486bh5 [1, -1, 1, 1254046, 206427251] [2] 1769472

## Rank

sage: E.rank()

The elliptic curves in class 45486.bl have rank $$0$$.

## Modular form 45486.2.a.bl

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 2q^{5} - q^{7} + q^{8} + 2q^{10} + 4q^{11} - 6q^{13} - q^{14} + q^{16} - 2q^{17} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.