Properties

Label 191984.a
Number of curves $1$
Conductor $191984$
CM no
Rank $1$

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

Elliptic curves in class 191984.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
191984.a1 191984a1 \([0, 0, 0, -7101211, -7253610806]\) \(2003092024307193/9529458688\) \(188403208029661560832\) \([]\) \(15956352\) \(2.7397\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 191984.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 191984.a do not have complex multiplication.

Modular form 191984.2.a.a

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