# Properties

 Label 83.a Number of curves $1$ Conductor $83$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 83.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
83.a1 83a1 $$[1, 1, 1, 1, 0]$$ $$103823/83$$ $$-83$$ $$[]$$ $$2$$ $$-0.94387$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 83.a1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 83.a do not have complex multiplication.

## Modular form83.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} - q^{4} - 2 q^{5} + q^{6} - 3 q^{7} + 3 q^{8} - 2 q^{9} + 2 q^{10} + 3 q^{11} + q^{12} - 6 q^{13} + 3 q^{14} + 2 q^{15} - q^{16} + 5 q^{17} + 2 q^{18} + 2 q^{19} + O(q^{20})$$