Properties

Label 405600a
Number of curves $1$
Conductor $405600$
CM no
Rank $1$

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

Elliptic curves in class 405600a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.a1 405600a1 \([0, -1, 0, 78867, 58397637]\) \(175616/4875\) \(-1505964408000000000\) \([]\) \(7741440\) \(2.1681\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 405600a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 405600a do not have complex multiplication.

Modular form 405600.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - 5q^{7} + q^{9} + q^{11} - 3q^{17} - 6q^{19} + O(q^{20})\)  Toggle raw display