# Properties

 Label 38640bd Number of curves $4$ Conductor $38640$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bd1")

sage: E.isogeny_class()

## Elliptic curves in class 38640bd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.g3 38640bd1 $$[0, -1, 0, -2033976, -1195140240]$$ $$-227196402372228188089/19338934824115200$$ $$-79212277039575859200$$ $$[2]$$ $$1105920$$ $$2.5631$$ $$\Gamma_0(N)$$-optimal
38640.g2 38640bd2 $$[0, -1, 0, -33181496, -73557058704]$$ $$986396822567235411402169/6336721794060000$$ $$25955212468469760000$$ $$[2]$$ $$2211840$$ $$2.9096$$
38640.g4 38640bd3 $$[0, -1, 0, 12058584, -48234384]$$ $$47342661265381757089751/27397579603968000000$$ $$-112220486057852928000000$$ $$[2]$$ $$3317760$$ $$3.1124$$
38640.g1 38640bd4 $$[0, -1, 0, -48234536, -337641360]$$ $$3029968325354577848895529/1753440696000000000000$$ $$7182093090816000000000000$$ $$[2]$$ $$6635520$$ $$3.4589$$

## Rank

sage: E.rank()

The elliptic curves in class 38640bd have rank $$0$$.

## Complex multiplication

The elliptic curves in class 38640bd do not have complex multiplication.

## Modular form 38640.2.a.bd

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} - 4q^{13} + q^{15} - 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.