# Properties

 Label 51600.ck Number of curves $1$ Conductor $51600$ CM no Rank $0$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ck1")

sage: E.isogeny_class()

## Elliptic curves in class 51600.ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
51600.ck1 51600v1 $$[0, 1, 0, -33, -117]$$ $$-640000/387$$ $$-2476800$$ $$[]$$ $$7296$$ $$-0.070981$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 51600.ck1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 51600.ck do not have complex multiplication.

## Modular form 51600.2.a.ck

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{7} + q^{9} + 6q^{13} - 3q^{17} - 2q^{19} + O(q^{20})$$