Properties

Label 1400j
Number of curves $1$
Conductor $1400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 1400j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1400.k1 1400j1 \([0, 1, 0, -33, 563]\) \(-1024/35\) \(-140000000\) \([]\) \(384\) \(0.24339\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1400j1 has rank \(1\).

Complex multiplication

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

Modular form 1400.2.a.j

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