# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("dy1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.dy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.dy1 87120df2 $$[0, 0, 0, -11735427, -15228016254]$$ $$685429074513/12500000$$ $$3259626888038400000000$$ $$$$ $$4055040$$ $$2.9230$$
87120.dy2 87120df1 $$[0, 0, 0, -1513347, 356566914]$$ $$1469878353/640000$$ $$166892896667566080000$$ $$$$ $$2027520$$ $$2.5764$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.dy

sage: E.q_eigenform(10)

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