Properties

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

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 1400k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1400.c1 1400k1 \([0, 1, 0, -28, -147]\) \(-6288640/16807\) \(-6722800\) \([]\) \(240\) \(-0.0024397\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1400k1 has rank \(1\).

Complex multiplication

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

Modular form 1400.2.a.k

sage: E.q_eigenform(10)
 
\(q - 2 q^{3} + q^{7} + q^{9} + q^{11} - 4 q^{13} + 6 q^{19} + O(q^{20})\) Copy content Toggle raw display