Properties

 Label 435344f Number of curves $1$ Conductor $435344$ CM no Rank $1$

Related objects

Show commands: SageMath
sage: E = EllipticCurve("f1")

sage: E.isogeny_class()

Elliptic curves in class 435344f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
435344.f1 435344f1 $$[0, 1, 0, -493029, 132216787]$$ $$670381355008/5025293$$ $$99353106350231552$$ $$[]$$ $$5107200$$ $$2.0916$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 435344f1 has rank $$1$$.

Complex multiplication

The elliptic curves in class 435344f do not have complex multiplication.

Modular form 435344.2.a.f

sage: E.q_eigenform(10)

$$q - 2q^{3} - 2q^{5} + q^{7} + q^{9} + 3q^{11} + 4q^{15} + q^{17} - 4q^{19} + O(q^{20})$$