# Properties

 Label 229320cs Number of curves $1$ Conductor $229320$ CM no Rank $0$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("cs1")

sage: E.isogeny_class()

## Elliptic curves in class 229320cs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.c1 229320cs1 $$[0, 0, 0, -2058, -103243]$$ $$-387072/1625$$ $$-4046890302000$$ $$[]$$ $$467712$$ $$1.1042$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 229320cs1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 229320cs do not have complex multiplication.

## Modular form 229320.2.a.cs

sage: E.q_eigenform(10)

$$q - q^{5} - 5q^{11} - q^{13} - 7q^{17} + 6q^{19} + O(q^{20})$$