# Properties

 Label 38640.dc Number of curves $2$ Conductor $38640$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("dc1")

sage: E.isogeny_class()

## Elliptic curves in class 38640.dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
38640.dc1 38640db2 $$[0, 1, 0, -63680, -6202572]$$ $$6972359126281921/5071500000$$ $$20772864000000$$ $$$$ $$184320$$ $$1.4900$$
38640.dc2 38640db1 $$[0, 1, 0, -4800, -55500]$$ $$2986606123201/1421952000$$ $$5824315392000$$ $$$$ $$92160$$ $$1.1434$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 38640.2.a.dc

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + q^{7} + q^{9} + 2q^{11} - 6q^{13} + q^{15} + 4q^{17} + 2q^{19} + O(q^{20})$$ ## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 