Properties

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

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 41405.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41405.d1 41405p1 \([1, -1, 1, 813, -107376]\) \(251559/21125\) \(-4996350666125\) \([]\) \(120960\) \(1.1161\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41405.d1 has rank \(1\).

Complex multiplication

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

Modular form 41405.2.a.d

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