Properties

Label 41070u
Number of curves $1$
Conductor $41070$
CM no
Rank $1$

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

Elliptic curves in class 41070u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.t1 41070u1 \([1, 1, 1, 77865269, 764831199353]\) \(401734898254403/2176782336000\) \(-282898419541751873359872000\) \([]\) \(21098880\) \(3.7577\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41070u1 has rank \(1\).

Complex multiplication

The elliptic curves in class 41070u do not have complex multiplication.

Modular form 41070.2.a.u

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