# Properties

 Label 108900.dc Number of curves $4$ Conductor $108900$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 108900.dc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
108900.dc1 108900bw4 $$[0, 0, 0, -6806150175, -216122709888250]$$ $$6749703004355978704/5671875$$ $$29300179546687500000000$$ $$[2]$$ $$39813120$$ $$4.0465$$
108900.dc2 108900bw3 $$[0, 0, 0, -425290800, -3378477466375]$$ $$-26348629355659264/24169921875$$ $$-7803669978698730468750000$$ $$[2]$$ $$19906560$$ $$3.7000$$
108900.dc3 108900bw2 $$[0, 0, 0, -85931175, -282320739250]$$ $$13584145739344/1195803675$$ $$6177368573899944300000000$$ $$[2]$$ $$13271040$$ $$3.4972$$
108900.dc4 108900bw1 $$[0, 0, 0, 5953200, -20542154875]$$ $$72268906496/606436875$$ $$-195798449820739218750000$$ $$[2]$$ $$6635520$$ $$3.1506$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 108900.dc have rank $$0$$.

## Complex multiplication

The elliptic curves in class 108900.dc do not have complex multiplication.

## Modular form 108900.2.a.dc

sage: E.q_eigenform(10)

$$q + 2q^{7} + 2q^{13} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.