Properties

Label 1694.f
Number of curves $1$
Conductor $1694$
CM no
Rank $0$

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

Elliptic curves in class 1694.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1694.f1 1694h1 \([1, 1, 1, 3, 1]\) \(24167/14\) \(-1694\) \([]\) \(96\) \(-0.69097\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1694.f1 has rank \(0\).

Complex multiplication

The elliptic curves in class 1694.f do not have complex multiplication.

Modular form 1694.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 2 q^{5} - q^{6} + q^{7} + q^{8} - 2 q^{9} + 2 q^{10} - q^{12} + 7 q^{13} + q^{14} - 2 q^{15} + q^{16} - 2 q^{18} - q^{19} + O(q^{20})\) Copy content Toggle raw display