Properties

Label 11830a
Number of curves $1$
Conductor $11830$
CM no
Rank $0$

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

Elliptic curves in class 11830a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
11830.j1 11830a1 \([1, 0, 1, 20276, -3535478]\) \(86938307/560000\) \(-5938519648880000\) \([]\) \(104832\) \(1.7085\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 11830a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 11830a do not have complex multiplication.

Modular form 11830.2.a.a

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