Properties

Label 41405.g
Number of curves $1$
Conductor $41405$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 41405.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41405.g1 41405c1 \([1, -1, 1, 39852, 36750172]\) \(251559/21125\) \(-587815659518940125\) \([]\) \(846720\) \(2.0891\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41405.g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 41405.g do not have complex multiplication.

Modular form 41405.2.a.g

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