# Properties

 Label 87120.fe Number of curves $2$ Conductor $87120$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fe1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.fe

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.fe1 87120fo2 $$[0, 0, 0, -475167, -126117574]$$ $$-296587984/125$$ $$-5000563975968000$$ $$[]$$ $$570240$$ $$1.9735$$
87120.fe2 87120fo1 $$[0, 0, 0, 3993, -673486]$$ $$176/5$$ $$-200022559038720$$ $$[]$$ $$190080$$ $$1.4242$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.fe

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 