# Properties

 Label 229320.dq Number of curves $4$ Conductor $229320$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("dq1")

sage: E.isogeny_class()

## Elliptic curves in class 229320.dq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.dq1 229320dc4 $$[0, 0, 0, -8573187, -9661815394]$$ $$396738988420322/2985255$$ $$524357102685911040$$ $$[2]$$ $$6291456$$ $$2.5755$$
229320.dq2 229320dc2 $$[0, 0, 0, -546987, -144347434]$$ $$206081497444/16769025$$ $$1472731368654873600$$ $$[2, 2]$$ $$3145728$$ $$2.2289$$
229320.dq3 229320dc1 $$[0, 0, 0, -114807, 12361034]$$ $$7622072656/1404585$$ $$30839246608584960$$ $$[2]$$ $$1572864$$ $$1.8824$$ $$\Gamma_0(N)$$-optimal
229320.dq4 229320dc3 $$[0, 0, 0, 564333, -656221426]$$ $$113157757438/1124589375$$ $$-197533016906883840000$$ $$[2]$$ $$6291456$$ $$2.5755$$

## Rank

sage: E.rank()

The elliptic curves in class 229320.dq have rank $$0$$.

## Complex multiplication

The elliptic curves in class 229320.dq do not have complex multiplication.

## Modular form 229320.2.a.dq

sage: E.q_eigenform(10)

$$q + q^{5} - q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.