# Properties

 Label 87120.e Number of curves $4$ Conductor $87120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.e1 87120bk4 $$[0, 0, 0, -116523, 15309162]$$ $$132304644/5$$ $$6612316001280$$ $$$$ $$327680$$ $$1.5460$$
87120.e2 87120bk2 $$[0, 0, 0, -7623, 215622]$$ $$148176/25$$ $$8265395001600$$ $$[2, 2]$$ $$163840$$ $$1.1995$$
87120.e3 87120bk1 $$[0, 0, 0, -2178, -35937]$$ $$55296/5$$ $$103317437520$$ $$$$ $$81920$$ $$0.85289$$ $$\Gamma_0(N)$$-optimal
87120.e4 87120bk3 $$[0, 0, 0, 14157, 1221858]$$ $$237276/625$$ $$-826539500160000$$ $$$$ $$327680$$ $$1.5460$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.e

sage: E.q_eigenform(10)

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

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 