# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 85176ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
85176.bs4 85176ce1 [0, 0, 0, 1521, -118638] [2] 147456 $$\Gamma_0(N)$$-optimal
85176.bs3 85176ce2 [0, 0, 0, -28899, -1779570] [2, 2] 294912
85176.bs2 85176ce3 [0, 0, 0, -89739, 8186022] [2] 589824
85176.bs1 85176ce4 [0, 0, 0, -454779, -118044810] [2] 589824

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 85176.2.a.ce

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 Cremona 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 Cremona labels.