Properties

Label 41785.a
Number of curves $1$
Conductor $41785$
CM no
Rank $3$

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

Elliptic curves in class 41785.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41785.a1 41785a1 \([0, 1, 1, -286, 1766]\) \(2596207734784/5223125\) \(5223125\) \([]\) \(23232\) \(0.17615\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41785.a1 has rank \(3\).

Complex multiplication

The elliptic curves in class 41785.a do not have complex multiplication.

Modular form 41785.2.a.a

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