# Properties

 Label 289800.bz Number of curves $4$ Conductor $289800$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bz1")

sage: E.isogeny_class()

## Elliptic curves in class 289800.bz

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.bz1 289800bz3 $$[0, 0, 0, -41733075, 103769252750]$$ $$344577854816148242/2716875$$ $$63379260000000000$$ $$$$ $$11796480$$ $$2.8149$$
289800.bz2 289800bz2 $$[0, 0, 0, -2610075, 1619099750]$$ $$168591300897604/472410225$$ $$5510192864400000000$$ $$[2, 2]$$ $$5898240$$ $$2.4684$$
289800.bz3 289800bz4 $$[0, 0, 0, -1575075, 2915954750]$$ $$-18524646126002/146738831715$$ $$-3423123466247520000000$$ $$$$ $$11796480$$ $$2.8149$$
289800.bz4 289800bz1 $$[0, 0, 0, -229575, 2740250]$$ $$458891455696/264449745$$ $$771135456420000000$$ $$$$ $$2949120$$ $$2.1218$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 289800.bz have rank $$0$$.

## Complex multiplication

The elliptic curves in class 289800.bz do not have complex multiplication.

## Modular form 289800.2.a.bz

sage: E.q_eigenform(10)

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