# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ex1")

sage: E.isogeny_class()

## Elliptic curves in class 87120.ex

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87120.ex1 87120fm2 $$[0, 0, 0, -83127, -9149294]$$ $$192143824/1815$$ $$600067677116160$$ $$$$ $$368640$$ $$1.6564$$
87120.ex2 87120fm1 $$[0, 0, 0, -1452, -344729]$$ $$-16384/2475$$ $$-51142131572400$$ $$$$ $$184320$$ $$1.3099$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 87120.2.a.ex

sage: E.q_eigenform(10)

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