# Properties

 Label 123840fy Number of curves $2$ Conductor $123840$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("fy1")

sage: E.isogeny_class()

## Elliptic curves in class 123840fy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
123840.fw2 123840fy1 $$[0, 0, 0, -21612, 820816]$$ $$5841725401/1857600$$ $$354992888217600$$ $$$$ $$442368$$ $$1.4958$$ $$\Gamma_0(N)$$-optimal
123840.fw1 123840fy2 $$[0, 0, 0, -136812, -18855344]$$ $$1481933914201/53916840$$ $$10303668580515840$$ $$$$ $$884736$$ $$1.8423$$

## Rank

sage: E.rank()

The elliptic curves in class 123840fy have rank $$0$$.

## Complex multiplication

The elliptic curves in class 123840fy do not have complex multiplication.

## Modular form 123840.2.a.fy

sage: E.q_eigenform(10)

$$q + q^{5} + 2q^{7} + 2q^{11} + 2q^{13} + 4q^{17} - 6q^{19} + O(q^{20})$$ ## 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 Cremona 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 Cremona labels. 