# Properties

 Label 605c Number of curves $1$ Conductor $605$ CM no Rank $1$

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 605c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
605.a1 605c1 [1, -1, 1, -12, 36] [] 120 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 605c1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 605c do not have complex multiplication.

## Modular form605.2.a.c

sage: E.q_eigenform(10)

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