# Properties

 Label 85176.bi Number of curves $2$ Conductor $85176$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bi1")

sage: E.isogeny_class()

## Elliptic curves in class 85176.bi

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.bi1 85176bp2 $$[0, 0, 0, -1755, 28054]$$ $$4920750/49$$ $$5952780288$$ $$$$ $$52224$$ $$0.69422$$
85176.bi2 85176bp1 $$[0, 0, 0, -195, -338]$$ $$13500/7$$ $$425198592$$ $$$$ $$26112$$ $$0.34765$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 85176.2.a.bi

sage: E.q_eigenform(10)

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