Properties

 Label 8619h Number of curves $1$ Conductor $8619$ CM no Rank $0$

Related objects

Show commands for: SageMath
sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

Elliptic curves in class 8619h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8619.a1 8619h1 $$[0, -1, 1, -9520, -632838]$$ $$-692224/867$$ $$-119523312433083$$ $$[]$$ $$68016$$ $$1.3946$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 8619h1 has rank $$0$$.

Complex multiplication

The elliptic curves in class 8619h do not have complex multiplication.

Modular form8619.2.a.h

sage: E.q_eigenform(10)

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