# Properties

 Label 60690bf Number of curves $4$ Conductor $60690$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 60690bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
60690.bf3 60690bf1 [1, 0, 1, -1018, -7972] [2] 73728 $$\Gamma_0(N)$$-optimal
60690.bf2 60690bf2 [1, 0, 1, -6798, 209356] [2, 2] 147456
60690.bf4 60690bf3 [1, 0, 1, 1872, 708748] [2] 294912
60690.bf1 60690bf4 [1, 0, 1, -107948, 13642076] [2] 294912

## Rank

sage: E.rank()

The elliptic curves in class 60690bf have rank $$0$$.

## Complex multiplication

The elliptic curves in class 60690bf do not have complex multiplication.

## Modular form 60690.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + q^{7} - q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - 2q^{13} - q^{14} + q^{15} + q^{16} - q^{18} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.