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Properties

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

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Show commands: SageMath
Copy content sage:E = EllipticCurve("u1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 451770.u1 has rank \(0\).

Complex multiplication

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

Modular form 451770.2.a.u

Copy content sage:E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} - q^{13} - q^{14} - q^{15} + q^{16} + 7 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Elliptic curves in class 451770.u

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
451770.u1 451770u1 \([1, 0, 1, -677684, -92333518]\) \(13415107060081/6329664000\) \(16240186084896576000\) \([]\) \(11819520\) \(2.3803\) \(\Gamma_0(N)\)-optimal