# Properties

 Label 413712.ey Number of curves $1$ Conductor $413712$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ey1")

sage: E.isogeny_class()

## Elliptic curves in class 413712.ey

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
413712.ey1 413712ey1 $$[0, 0, 0, -1370928, -1099027280]$$ $$-692224/867$$ $$-356894698552186908672$$ $$[]$$ $$21765120$$ $$2.6370$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 413712.ey1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 413712.ey do not have complex multiplication.

## Modular form 413712.2.a.ey

sage: E.q_eigenform(10)

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