# Properties

 Label 22050df Number of curves $1$ Conductor $22050$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("df1")

sage: E.isogeny_class()

## Elliptic curves in class 22050df

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.de1 22050df1 [1, -1, 1, 1975, 96457] [] 59904 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 22050df1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 22050df do not have complex multiplication.

## Modular form 22050.2.a.df

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{8} - 4q^{11} - 3q^{13} + q^{16} + 7q^{17} + 6q^{19} + O(q^{20})$$