# Properties

 Label 58800gc Number of curves $1$ Conductor $58800$ CM no Rank $1$

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("gc1")

sage: E.isogeny_class()

## Elliptic curves in class 58800gc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
58800.h1 58800gc1 $$[0, -1, 0, -489918, 132151167]$$ $$-805661175040/729$$ $$-11767111801200$$ $$[]$$ $$387072$$ $$1.8063$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 58800gc1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 58800gc do not have complex multiplication.

## Modular form 58800.2.a.gc

sage: E.q_eigenform(10)

$$q - q^{3} + q^{9} - 5q^{11} - 2q^{13} - 2q^{17} - 6q^{19} + O(q^{20})$$