Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 1694.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1694.a1 1694a1 \([1, 1, 0, 361, 235]\) \(24167/14\) \(-3001024334\) \([]\) \(1056\) \(0.50798\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1694.a1 has rank \(0\).

Complex multiplication

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

Modular form 1694.2.a.a

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