# Properties

 Label 352800bf Number of curves $4$ Conductor $352800$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 352800bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
352800.bf3 352800bf1 $$[0, 0, 0, -70325722425, -7178262572117000]$$ $$448487713888272974160064/91549016015625$$ $$7851803985027031640625000000$$ $$[2, 2]$$ $$990904320$$ $$4.7404$$ $$\Gamma_0(N)$$-optimal
352800.bf2 352800bf2 $$[0, 0, 0, -70566894300, -7126549533992000]$$ $$7079962908642659949376/100085966990454375$$ $$549375049939540209358680000000000$$ $$[2]$$ $$1981808640$$ $$5.0870$$
352800.bf4 352800bf3 $$[0, 0, 0, -70084605675, -7229928345956750]$$ $$-55486311952875723077768/801237030029296875$$ $$-549751936537386474609375000000000$$ $$[2]$$ $$1981808640$$ $$5.0870$$
352800.bf1 352800bf4 $$[0, 0, 0, -1125211503675, -459408851879773250]$$ $$229625675762164624948320008/9568125$$ $$6564967731945000000000$$ $$[2]$$ $$1981808640$$ $$5.0870$$

## Rank

sage: E.rank()

The elliptic curves in class 352800bf have rank $$0$$.

## Complex multiplication

The elliptic curves in class 352800bf do not have complex multiplication.

## Modular form 352800.2.a.bf

sage: E.q_eigenform(10)

$$q - 4q^{11} - 6q^{13} - 6q^{17} - 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.