# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("en1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.en

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.en1 87120fs2 $$[0, 0, 0, -33776787, 75329028434]$$ $$55025549689/192000$$ $$14870157093080137728000$$ $$[]$$ $$5474304$$ $$3.1171$$
87120.en2 87120fs1 $$[0, 0, 0, -2152227, -1132832734]$$ $$14235529/1080$$ $$83644633648575774720$$ $$[]$$ $$1824768$$ $$2.5678$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.en

sage: E.q_eigenform(10)

$$q + q^{5} - q^{7} + q^{13} - 3q^{17} - q^{19} + O(q^{20})$$ ## 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. 