Properties

Label 446.a
Number of curves $1$
Conductor $446$
CM no
Rank $2$

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

Elliptic curves in class 446.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
446.a1 446d1 \([1, -1, 0, -4, 4]\) \(8120601/892\) \(892\) \([]\) \(88\) \(-0.70040\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 446.a1 has rank \(2\).

Complex multiplication

The elliptic curves in class 446.a do not have complex multiplication.

Modular form 446.2.a.a

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