# Properties

 Label 154800bw Number of curves $2$ Conductor $154800$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 154800bw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
154800.br2 154800bw1 $$[0, 0, 0, -135075, 12825250]$$ $$5841725401/1857600$$ $$86668185600000000$$ $$$$ $$1327104$$ $$1.9539$$ $$\Gamma_0(N)$$-optimal
154800.br1 154800bw2 $$[0, 0, 0, -855075, -294614750]$$ $$1481933914201/53916840$$ $$2515544087040000000$$ $$$$ $$2654208$$ $$2.3005$$

## Rank

sage: E.rank()

The elliptic curves in class 154800bw have rank $$1$$.

## Complex multiplication

The elliptic curves in class 154800bw do not have complex multiplication.

## Modular form 154800.2.a.bw

sage: E.q_eigenform(10)

$$q - 2q^{7} - 2q^{11} + 2q^{13} - 4q^{17} + 6q^{19} + O(q^{20})$$ ## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 