# Properties

 Label 338130by Number of curves $1$ Conductor $338130$ CM no Rank $1$

# Learn more

Show commands for: SageMath
sage: E = EllipticCurve("by1")

sage: E.isogeny_class()

## Elliptic curves in class 338130by

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
338130.by1 338130by1 $$[1, -1, 0, -11529, -506655]$$ $$-804441463921/66832740$$ $$-14080388495940$$ $$[]$$ $$967680$$ $$1.2685$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 338130by1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 338130by do not have complex multiplication.

## Modular form 338130.2.a.by

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} + 3q^{11} - q^{13} - 2q^{14} + q^{16} + 5q^{19} + O(q^{20})$$