# Properties

 Label 124950.fy Number of curves $2$ Conductor $124950$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 124950.fy

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
124950.fy1 124950fn2 $$[1, 1, 1, -635188, -143809219]$$ $$15417797707369/4080067320$$ $$7500247502041875000$$ $$[2]$$ $$2654208$$ $$2.3304$$
124950.fy2 124950fn1 $$[1, 1, 1, 99812, -14449219]$$ $$59822347031/83966400$$ $$-154352546775000000$$ $$[2]$$ $$1327104$$ $$1.9838$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 124950.fy have rank $$0$$.

## Complex multiplication

The elliptic curves in class 124950.fy do not have complex multiplication.

## Modular form 124950.2.a.fy

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 2q^{11} - q^{12} - 2q^{13} + q^{16} + q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.