Properties

Label 444675.fj
Number of curves $1$
Conductor $444675$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("fj1")
 
E.isogeny_class()
 

Elliptic curves in class 444675.fj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
444675.fj1 444675fj1 \([1, 1, 0, -185000, -32730375]\) \(-7558595228569/597871125\) \(-55387154689453125\) \([]\) \(3483648\) \(1.9597\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 444675.fj1 has rank \(1\).

Complex multiplication

The elliptic curves in class 444675.fj do not have complex multiplication.

Modular form 444675.2.a.fj

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} - q^{6} - 3 q^{8} + q^{9} + q^{12} - 4 q^{13} - q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display