Properties

Label 41070.z
Number of curves $1$
Conductor $41070$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("z1")
 
E.isogeny_class()
 

Elliptic curves in class 41070.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.z1 41070x1 \([1, 1, 1, -39045, 5262820875]\) \(-1369/2488320\) \(-11965296665574782023680\) \([]\) \(4102560\) \(2.9152\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41070.z1 has rank \(1\).

Complex multiplication

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

Modular form 41070.2.a.z

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