# Properties

 Label 85176.bs Number of curves $4$ Conductor $85176$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

## Elliptic curves in class 85176.bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.bs1 85176ce4 $$[0, 0, 0, -454779, -118044810]$$ $$1443468546/7$$ $$50444710557696$$ $$[2]$$ $$589824$$ $$1.8297$$
85176.bs2 85176ce3 $$[0, 0, 0, -89739, 8186022]$$ $$11090466/2401$$ $$17302535721289728$$ $$[2]$$ $$589824$$ $$1.8297$$
85176.bs3 85176ce2 $$[0, 0, 0, -28899, -1779570]$$ $$740772/49$$ $$176556486951936$$ $$[2, 2]$$ $$294912$$ $$1.4832$$
85176.bs4 85176ce1 $$[0, 0, 0, 1521, -118638]$$ $$432/7$$ $$-6305588819712$$ $$[2]$$ $$147456$$ $$1.1366$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 85176.bs have rank $$0$$.

## Complex multiplication

The elliptic curves in class 85176.bs do not have complex multiplication.

## Modular form 85176.2.a.bs

sage: E.q_eigenform(10)

$$q + 2q^{5} + q^{7} - 4q^{11} + 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.