# Properties

 Label 87120.fo Number of curves $2$ Conductor $87120$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("fo1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.fo

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.fo1 87120de2 $$[0, 0, 0, -96987, 11441034]$$ $$685429074513/12500000$$ $$1839974400000000$$ $$[2]$$ $$368640$$ $$1.7240$$
87120.fo2 87120de1 $$[0, 0, 0, -12507, -267894]$$ $$1469878353/640000$$ $$94206689280000$$ $$[2]$$ $$184320$$ $$1.3775$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 87120.fo have rank $$1$$.

## Complex multiplication

The elliptic curves in class 87120.fo do not have complex multiplication.

## Modular form 87120.2.a.fo

sage: E.q_eigenform(10)

$$q + q^{5} + 2q^{7} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.