# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bm1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.bm

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.bm1 87120ct1 $$[0, 0, 0, -29403, 1807498]$$ $$14348907/1100$$ $$215512521523200$$ $$$$ $$184320$$ $$1.4950$$ $$\Gamma_0(N)$$-optimal
87120.bm2 87120ct2 $$[0, 0, 0, 28677, 8068522]$$ $$13312053/151250$$ $$-29632971709440000$$ $$$$ $$368640$$ $$1.8416$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.bm

sage: E.q_eigenform(10)

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