Properties

Label 400710.u
Number of curves $1$
Conductor $400710$
CM no
Rank $0$

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

Elliptic curves in class 400710.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
400710.u1 400710u1 \([1, 0, 1, -37913, -2876644]\) \(-128100283921/1687200\) \(-79375810423200\) \([]\) \(1728000\) \(1.4753\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 400710.u1 has rank \(0\).

Complex multiplication

The elliptic curves in class 400710.u do not have complex multiplication.

Modular form 400710.2.a.u

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