# Properties

 Label 270802.k Number of curves $1$ Conductor $270802$ CM no Rank $0$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 270802.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
270802.k1 270802k1 $$[1, -1, 0, 9132157712, 117242784756992]$$ $$5805798253576046271027/3769183309498679296$$ $$-54680092480706364912736585908224$$ $$[]$$ $$1830624768$$ $$4.7788$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 270802.k1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 270802.k do not have complex multiplication.

## Modular form 270802.2.a.k

sage: E.q_eigenform(10)

$$q - q^{2} + 3q^{3} + q^{4} + 3q^{5} - 3q^{6} - q^{7} - q^{8} + 6q^{9} - 3q^{10} - 5q^{11} + 3q^{12} + q^{13} + q^{14} + 9q^{15} + q^{16} - 2q^{17} - 6q^{18} + 4q^{19} + O(q^{20})$$ 