# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("fp1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.fp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.fp1 87120fy4 $$[0, 0, 0, -272246007, 1728981679106]$$ $$6749703004355978704/5671875$$ $$1875211490988000000$$ $$$$ $$6635520$$ $$3.2418$$
87120.fp2 87120fy3 $$[0, 0, 0, -17011632, 27027819731]$$ $$-26348629355659264/24169921875$$ $$-499434878636718750000$$ $$$$ $$3317760$$ $$2.8952$$
87120.fp3 87120fy2 $$[0, 0, 0, -3437247, 2258565914]$$ $$13584145739344/1195803675$$ $$395351588729596435200$$ $$$$ $$2211840$$ $$2.6925$$
87120.fp4 87120fy1 $$[0, 0, 0, 238128, 164337239]$$ $$72268906496/606436875$$ $$-12531100788527310000$$ $$$$ $$1105920$$ $$2.3459$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.fp

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 