# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ed1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.ed

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.ed1 87120bt2 $$[0, 0, 0, -388115607, -2942996692394]$$ $$14692827276345584/6075$$ $$2673301501552492800$$ $$[2]$$ $$8110080$$ $$3.3179$$
87120.ed2 87120bt1 $$[0, 0, 0, -24253482, -45999225569]$$ $$-57367289145344/36905625$$ $$-1015019163870712110000$$ $$[2]$$ $$4055040$$ $$2.9713$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.ed

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.