Properties

Label 4400i
Number of curves $1$
Conductor $4400$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 4400i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4400.j1 4400i1 \([0, -1, 0, 32, 32]\) \(13718/11\) \(-2816000\) \([]\) \(384\) \(-0.074549\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4400i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4400i do not have complex multiplication.

Modular form 4400.2.a.i

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