# Properties

 Label 19320.bb Number of curves $4$ Conductor $19320$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 19320.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
19320.bb1 19320l3 $$[0, 1, 0, -185480, -30808272]$$ $$344577854816148242/2716875$$ $$5564160000$$ $$$$ $$61440$$ $$1.4609$$
19320.bb2 19320l2 $$[0, 1, 0, -11600, -483600]$$ $$168591300897604/472410225$$ $$483748070400$$ $$[2, 2]$$ $$30720$$ $$1.1143$$
19320.bb3 19320l4 $$[0, 1, 0, -7000, -866320]$$ $$-18524646126002/146738831715$$ $$-300521127352320$$ $$$$ $$61440$$ $$1.4609$$
19320.bb4 19320l1 $$[0, 1, 0, -1020, -1152]$$ $$458891455696/264449745$$ $$67699134720$$ $$$$ $$15360$$ $$0.76776$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 19320.bb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 19320.bb do not have complex multiplication.

## Modular form 19320.2.a.bb

sage: E.q_eigenform(10)

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