# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 75712.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
75712.p1 75712cf1 $$[0, 1, 0, -3605, -154829]$$ $$-65536/91$$ $$-7196501917696$$ $$[]$$ $$129024$$ $$1.1594$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 75712.p1 has rank $$0$$.

## Complex multiplication

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

## Modular form 75712.2.a.p

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} - q^{7} + q^{9} + 4q^{11} - 2q^{15} - 2q^{17} + q^{19} + O(q^{20})$$