# Properties

 Label 450800ew Number of curves $1$ Conductor $450800$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("ew1")

sage: E.isogeny_class()

## Elliptic curves in class 450800ew

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450800.ew1 450800ew1 $$[0, 1, 0, -4254833, 8408909963]$$ $$-144814859264/435654247$$ $$-25627143252651500000000$$ $$[]$$ $$24944640$$ $$2.9866$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 450800ew1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 450800ew do not have complex multiplication.

## Modular form 450800.2.a.ew

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{9} + 3q^{11} - 3q^{13} - 3q^{17} - 2q^{19} + O(q^{20})$$