# Properties

 Label 75712.bg Number of curves $1$ Conductor $75712$ CM no Rank $0$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 75712.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.bg1 75712u1 $$[0, 0, 0, -4394, -742586]$$ $$-13824/343$$ $$-232789970236096$$ $$[]$$ $$179712$$ $$1.4374$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 75712.bg1 has rank $$0$$.

## Complex multiplication

The elliptic curves in class 75712.bg do not have complex multiplication.

## Modular form 75712.2.a.bg

sage: E.q_eigenform(10)

$$q - 3q^{5} - q^{7} - 3q^{9} - 2q^{11} + 2q^{17} + 3q^{19} + O(q^{20})$$