# Properties

 Label 68544.bm Number of curves $4$ Conductor $68544$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 68544.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
68544.bm1 68544en4 $$[0, 0, 0, -2925516, 1925979536]$$ $$14489843500598257/6246072$$ $$1193642947510272$$ $$$$ $$1179648$$ $$2.2356$$
68544.bm2 68544en3 $$[0, 0, 0, -391116, -49764976]$$ $$34623662831857/14438442312$$ $$2759229294627520512$$ $$$$ $$1179648$$ $$2.2356$$
68544.bm3 68544en2 $$[0, 0, 0, -183756, 29778320]$$ $$3590714269297/73410624$$ $$14028988716417024$$ $$[2, 2]$$ $$589824$$ $$1.8890$$
68544.bm4 68544en1 $$[0, 0, 0, 564, 1393040]$$ $$103823/4386816$$ $$-838333592764416$$ $$$$ $$294912$$ $$1.5424$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 68544.bm have rank $$0$$.

## Complex multiplication

The elliptic curves in class 68544.bm do not have complex multiplication.

## Modular form 68544.2.a.bm

sage: E.q_eigenform(10)

$$q - 2q^{5} + q^{7} + 6q^{13} - q^{17} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 