# Properties

 Label 405600gc Number of curves $1$ Conductor $405600$ CM no Rank $0$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("gc1")

sage: E.isogeny_class()

## Elliptic curves in class 405600gc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.gc1 405600gc1 $$[0, 1, 0, 377152, -2121332472]$$ $$43709080/14348907$$ $$-1947686083644611980800$$ $$[]$$ $$22913280$$ $$2.7642$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 405600gc1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 405600gc do not have complex multiplication.

## Modular form 405600.2.a.gc

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} + 4q^{11} - 6q^{17} + 7q^{19} + O(q^{20})$$