Properties

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

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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 form 1400.2.a.k

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{7} - 2q^{9} - 5q^{11} - q^{13} - 3q^{17} - 6q^{19} + O(q^{20}) \)