Properties

Label 11197.a
Number of curves $1$
Conductor $11197$
CM no
Rank $3$

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

Elliptic curves in class 11197.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11197.a1 11197a1 \([1, -1, 1, -6, 0]\) \(20346417/11197\) \(11197\) \([]\) \(2080\) \(-0.53244\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 11197.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 11197.a do not have complex multiplication.

Modular form 11197.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 3 q^{3} - q^{4} - 2 q^{5} + 3 q^{6} - 5 q^{7} + 3 q^{8} + 6 q^{9} + 2 q^{10} - 4 q^{11} + 3 q^{12} - 7 q^{13} + 5 q^{14} + 6 q^{15} - q^{16} - 2 q^{17} - 6 q^{18} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display