Properties

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

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

Elliptic curves in class 41405.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41405.a1 41405t1 \([0, 0, 1, -637, -32328]\) \(-1437696/21875\) \(-434933646875\) \([]\) \(144000\) \(0.91459\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 41405.a1 has rank \(1\).

Complex multiplication

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

Modular form 41405.2.a.a

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