# Properties

 Label 116886e Number of curves $1$ Conductor $116886$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 116886e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.d1 116886e1 $$[1, 1, 0, 41017, 384531]$$ $$4307673070511/2525789574$$ $$-4474590303505014$$ $$[]$$ $$691200$$ $$1.6925$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 116886e1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 116886e do not have complex multiplication.

## Modular form 116886.2.a.e

sage: E.q_eigenform(10)

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