# Properties

 Label 303450cf Number of curves $1$ Conductor $303450$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cf1")

sage: E.isogeny_class()

## Elliptic curves in class 303450cf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
303450.cf1 303450cf1 $$[1, 0, 1, 13098774, 7799200348]$$ $$2280364702703/1560674304$$ $$-170107584204773376000000$$ $$[]$$ $$44945280$$ $$3.1462$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 303450cf1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 303450cf do not have complex multiplication.

## Modular form 303450.2.a.cf

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{7} - q^{8} + q^{9} + 5q^{11} + q^{12} + q^{14} + q^{16} - q^{18} + 6q^{19} + O(q^{20})$$