# Properties

 Label 405600.z Number of curves $1$ Conductor $405600$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("z1")

sage: E.isogeny_class()

## Elliptic curves in class 405600.z

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.z1 405600z1 $$[0, -1, 0, -413768, -102734568]$$ $$-150061288/729$$ $$-38058732518976000$$ $$[]$$ $$4432896$$ $$2.0301$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 405600.z1 has rank $$1$$.

## Complex multiplication

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

## Modular form 405600.2.a.z

sage: E.q_eigenform(10)

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