Properties

 Label 489762fj Number of curves $1$ Conductor $489762$ CM no Rank $0$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("fj1")

sage: E.isogeny_class()

Elliptic curves in class 489762fj

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
489762.fj1 489762fj1 $$[1, -1, 1, 13834984, -13295304421]$$ $$83228502970940543/69854999176704$$ $$-245801842527687336543744$$ $$[]$$ $$71089920$$ $$3.1759$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 489762fj1 has rank $$0$$.

Complex multiplication

The elliptic curves in class 489762fj do not have complex multiplication.

Modular form 489762.2.a.fj

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + 3q^{10} + 4q^{11} + q^{14} + q^{16} + 4q^{17} + O(q^{20})$$