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Properties

Label 451770j
Number of curves $1$
Conductor $451770$
CM no
Rank $0$

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Show commands: SageMath
Copy content sage:E = EllipticCurve("j1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 451770j1 has rank \(0\).

Complex multiplication

The elliptic curves in class 451770j do not have complex multiplication.

Modular form 451770.2.a.j

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

Elliptic curves in class 451770j

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
451770.j1 451770j1 \([1, 1, 0, -3888837557, 93340545718701]\) \(-3470373537504830811203247721/532432701217612800\) \(-997864603746702422860800\) \([]\) \(335865600\) \(4.0103\) \(\Gamma_0(N)\)-optimal