Properties

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

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1400f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1400.d1 1400f1 \([0, -1, 0, 7, 157]\) \(1024/343\) \(-10976000\) \([]\) \(192\) \(0.030070\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1400f1 has rank \(1\).

Complex multiplication

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

Modular form 1400.2.a.f

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{7} - 2 q^{9} - q^{11} + q^{13} + 3 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display