Properties

Label 355743a
Number of curves $1$
Conductor $355743$
CM no
Rank $1$

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

Elliptic curves in class 355743a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
355743.a1 355743a1 \([0, 0, 1, -93351, -4164422]\) \(207474688/102789\) \(44572003575514101\) \([]\) \(5638528\) \(1.8877\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 355743a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 355743a do not have complex multiplication.

Modular form 355743.2.a.a

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