Properties

 Label 189618.w Number of curves $1$ Conductor $189618$ CM no Rank $0$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("w1")

sage: E.isogeny_class()

Elliptic curves in class 189618.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.w1 189618bg1 $$[1, 0, 1, -166469, -98542546]$$ $$-625422146089/4779238662$$ $$-3898571799584335302$$ $$[]$$ $$5286528$$ $$2.2502$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 189618.w1 has rank $$0$$.

Complex multiplication

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

Modular form 189618.2.a.w

sage: E.q_eigenform(10)

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