Properties

Label 443760.x
Number of curves $1$
Conductor $443760$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 443760.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
443760.x1 443760x1 \([0, -1, 0, -4319880, -3356835600]\) \(186222121/6000\) \(287249210022322176000\) \([]\) \(20805120\) \(2.6996\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 443760.x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 443760.x do not have complex multiplication.

Modular form 443760.2.a.x

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} - 3 q^{7} + q^{9} - q^{11} - 6 q^{13} - q^{15} + 6 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display