Properties

 Label 169050gr Number of curves $1$ Conductor $169050$ CM no Rank $1$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gr1")

sage: E.isogeny_class()

Elliptic curves in class 169050gr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169050.eb1 169050gr1 $$[1, 0, 1, 11142574, -9606244252]$$ $$83228502970940543/69854999176704$$ $$-128412043720938264000000$$ $$[]$$ $$20528640$$ $$3.1218$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 169050gr1 has rank $$1$$.

Complex multiplication

The elliptic curves in class 169050gr do not have complex multiplication.

Modular form 169050.2.a.gr

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4q^{11} + q^{12} - 3q^{13} + q^{16} - 4q^{17} - q^{18} + O(q^{20})$$