Properties

 Label 1400.k Number of curves $1$ Conductor $1400$ CM no Rank $1$

Related objects

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

sage: E.isogeny_class()

Elliptic curves in class 1400.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1400.k1 1400j1 [0, 1, 0, -33, 563] [] 384 $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curve 1400.k1 has rank $$1$$.

Complex multiplication

The elliptic curves in class 1400.k do not have complex multiplication.

Modular form1400.2.a.k

sage: E.q_eigenform(10)

$$q + q^{3} + q^{7} - 2q^{9} - 5q^{11} - q^{13} - 3q^{17} - 6q^{19} + O(q^{20})$$