# Properties

 Label 18720bj Number of curves $4$ Conductor $18720$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bj1")

sage: E.isogeny_class()

## Elliptic curves in class 18720bj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18720.bh3 18720bj1 $$[0, 0, 0, -597, -5236]$$ $$504358336/38025$$ $$1774094400$$ $$[2, 2]$$ $$6144$$ $$0.51993$$ $$\Gamma_0(N)$$-optimal
18720.bh1 18720bj2 $$[0, 0, 0, -9372, -349216]$$ $$30488290624/195$$ $$582266880$$ $$[2]$$ $$12288$$ $$0.86651$$
18720.bh2 18720bj3 $$[0, 0, 0, -1947, 26894]$$ $$2186875592/428415$$ $$159905041920$$ $$[2]$$ $$12288$$ $$0.86651$$
18720.bh4 18720bj4 $$[0, 0, 0, 573, -23254]$$ $$55742968/658125$$ $$-245643840000$$ $$[2]$$ $$12288$$ $$0.86651$$

## Rank

sage: E.rank()

The elliptic curves in class 18720bj have rank $$0$$.

## Complex multiplication

The elliptic curves in class 18720bj do not have complex multiplication.

## Modular form 18720.2.a.bj

sage: E.q_eigenform(10)

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

## 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.