Properties

 Label 189618.r Number of curves $1$ Conductor $189618$ CM no Rank $2$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

Elliptic curves in class 189618.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.r1 189618z1 $$[1, 0, 1, -5581, 162242]$$ $$-672937149625/10996722$$ $$-314077377042$$ $$[]$$ $$288000$$ $$1.0061$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 189618.r1 has rank $$2$$.

Complex multiplication

The elliptic curves in class 189618.r do not have complex multiplication.

Modular form 189618.2.a.r

sage: E.q_eigenform(10)

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