# Properties

 Label 1960.k Number of curves $1$ Conductor $1960$ CM no Rank $1$

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 1960.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1960.k1 1960f1 $$[0, 1, 0, -65, -1597]$$ $$-1024/35$$ $$-1054135040$$ $$[]$$ $$768$$ $$0.41162$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 1960.k1 has rank $$1$$.

## Complex multiplication

The elliptic curves in class 1960.k do not have complex multiplication.

## Modular form1960.2.a.k

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - 2 q^{9} - 5 q^{11} - q^{13} + q^{15} - 3 q^{17} + 6 q^{19} + O(q^{20})$$