Properties

Label 44233.a
Number of curves $1$
Conductor $44233$
CM no
Rank $3$

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

Elliptic curves in class 44233.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44233.a1 44233a1 \([1, 1, 1, -137, 600]\) \(-284500822033/21983801\) \(-21983801\) \([]\) \(14208\) \(0.15646\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 44233.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 44233.a do not have complex multiplication.

Modular form 44233.2.a.a

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