Properties

Label 52325n
Number of curves $1$
Conductor $52325$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 52325n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52325.n1 52325n1 \([0, 0, 1, -38275, -4038969]\) \(-396870925750272/221358574619\) \(-3458727728421875\) \([]\) \(803520\) \(1.6850\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 52325n1 has rank \(1\).

Complex multiplication

The elliptic curves in class 52325n do not have complex multiplication.

Modular form 52325.2.a.n

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