# Properties

 Label 47190m Number of curves $1$ Conductor $47190$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 47190m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
47190.q1 47190m1 $$[1, 1, 0, -2, 6516]$$ $$-14641/151632000$$ $$-18347472000$$ $$[]$$ $$36288$$ $$0.64828$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 47190m1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 47190m do not have complex multiplication.

## Modular form 47190.2.a.m

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + 2q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - q^{13} - 2q^{14} - q^{15} + q^{16} + 2q^{17} - q^{18} + O(q^{20})$$