# Properties

 Label 216384.ed Number of curves $1$ Conductor $216384$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ed1")

sage: E.isogeny_class()

## Elliptic curves in class 216384.ed

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
216384.ed1 216384eh1 $$[0, -1, 0, 28524991, 39341471457]$$ $$83228502970940543/69854999176704$$ $$-2154396594507624977793024$$ $$[]$$ $$36495360$$ $$3.3568$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 216384.ed1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 216384.ed do not have complex multiplication.

## Modular form 216384.2.a.ed

sage: E.q_eigenform(10)

$$q - q^{3} + 3q^{5} + q^{9} + 4q^{11} - 3q^{13} - 3q^{15} + 4q^{17} + O(q^{20})$$