# Properties

 Label 289800.bw Number of curves $2$ Conductor $289800$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bw1")

sage: E.isogeny_class()

## Elliptic curves in class 289800.bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
289800.bw1 289800bw1 $$[0, 0, 0, -19575, 290250]$$ $$10536048/5635$$ $$443654820000000$$ $$$$ $$1105920$$ $$1.5018$$ $$\Gamma_0(N)$$-optimal
289800.bw2 289800bw2 $$[0, 0, 0, 74925, 2274750]$$ $$147704148/92575$$ $$-29154459600000000$$ $$$$ $$2211840$$ $$1.8483$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 289800.2.a.bw

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 