Properties

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

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 41070a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41070.c1 41070a1 \([1, 1, 0, -13718, -3482892]\) \(-81289/1440\) \(-5057970413646240\) \([]\) \(266400\) \(1.6944\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41070a1 has rank \(1\).

Complex multiplication

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

Modular form 41070.2.a.a

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