Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("r1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 405600r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
405600.r1 405600r1 \([0, -1, 0, -5633, -71343663]\) \(-1600/177957\) \(-2198948989985280000\) \([]\) \(7741440\) \(2.1984\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 405600r1 has rank \(1\).

Complex multiplication

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

Modular form 405600.2.a.r

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3q^{7} + q^{9} - 5q^{11} - 5q^{17} - 4q^{19} + O(q^{20})\)  Toggle raw display