# Properties

 Label 450840f Number of curves $1$ Conductor $450840$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

## Elliptic curves in class 450840f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
450840.f1 450840f1 $$[0, -1, 0, 300464, -37505735]$$ $$7767586344704/6060234375$$ $$-2340469206123750000$$ $$[]$$ $$6967296$$ $$2.2127$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 450840f1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 450840f do not have complex multiplication.

## Modular form 450840.2.a.f

sage: E.q_eigenform(10)

$$q - q^{3} - q^{5} - q^{7} + q^{9} + 3q^{11} + q^{13} + q^{15} + q^{19} + O(q^{20})$$