Properties

Label 1694e
Number of curves $1$
Conductor $1694$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("e1")
 
E.isogeny_class()
 

Elliptic curves in class 1694e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1694.h1 1694e1 \([1, -1, 1, -6073, 332313]\) \(-115538049/153664\) \(-32939243089984\) \([]\) \(3168\) \(1.2866\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 1694e1 has rank \(1\).

Complex multiplication

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

Modular form 1694.2.a.e

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - q^{7} + q^{8} - 3 q^{9} - q^{10} - q^{13} - q^{14} + q^{16} - q^{17} - 3 q^{18} + O(q^{20})\) Copy content Toggle raw display