# Properties

 Label 388416dt Number of curves $1$ Conductor $388416$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dt1")

sage: E.isogeny_class()

## Elliptic curves in class 388416dt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
388416.dt1 388416dt1 $$[0, -1, 0, 116031, 6462657]$$ $$2280364702703/1560674304$$ $$-118236085972107264$$ $$[]$$ $$4700160$$ $$1.9646$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 388416dt1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 388416dt do not have complex multiplication.

## Modular form 388416.2.a.dt

sage: E.q_eigenform(10)

$$q - q^{3} + 3q^{5} - q^{7} + q^{9} + 5q^{11} - 3q^{15} - 6q^{19} + O(q^{20})$$