# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("cd1")

sage: E.isogeny_class()

## Elliptic curves in class 85176.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
85176.cd1 85176bj1 $$[0, 0, 0, -14703, -681070]$$ $$10536048/91$$ $$3036024246528$$ $$$$ $$301056$$ $$1.2195$$ $$\Gamma_0(N)$$-optimal
85176.cd2 85176bj2 $$[0, 0, 0, -4563, -1603810]$$ $$-78732/8281$$ $$-1105112825736192$$ $$$$ $$602112$$ $$1.5661$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 85176.2.a.cd

sage: E.q_eigenform(10)

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