# Properties

 Label 58800bf Number of curves $6$ Conductor $58800$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 58800bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.o5 58800bf1 $$[0, -1, 0, -18783, 4082562]$$ $$-24918016/229635$$ $$-6754082028750000$$ $$[2]$$ $$294912$$ $$1.7199$$ $$\Gamma_0(N)$$-optimal
58800.o4 58800bf2 $$[0, -1, 0, -514908, 142005312]$$ $$32082281296/99225$$ $$46694888100000000$$ $$[2, 2]$$ $$589824$$ $$2.0664$$
58800.o3 58800bf3 $$[0, -1, 0, -735408, 8823312]$$ $$23366901604/13505625$$ $$25422772410000000000$$ $$[2, 2]$$ $$1179648$$ $$2.4130$$
58800.o1 58800bf4 $$[0, -1, 0, -8232408, 9094305312]$$ $$32779037733124/315$$ $$592950960000000$$ $$[4]$$ $$1179648$$ $$2.4130$$
58800.o6 58800bf5 $$[0, -1, 0, 2939592, 67623312]$$ $$746185003198/432360075$$ $$-1627735374837600000000$$ $$[2]$$ $$2359296$$ $$2.7596$$
58800.o2 58800bf6 $$[0, -1, 0, -7938408, -8577152688]$$ $$14695548366242/57421875$$ $$216180037500000000000$$ $$[2]$$ $$2359296$$ $$2.7596$$

## Rank

sage: E.rank()

The elliptic curves in class 58800bf have rank $$0$$.

## Complex multiplication

The elliptic curves in class 58800bf do not have complex multiplication.

## Modular form 58800.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 4q^{11} - 2q^{13} + 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.