Properties

Label 297825cd
Number of curves $1$
Conductor $297825$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("cd1")
 
E.isogeny_class()
 

Elliptic curves in class 297825cd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297825.cd1 297825cd1 \([1, 0, 1, 524, -64777]\) \(2828663/323433\) \(-1824364265625\) \([]\) \(552960\) \(1.0321\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 297825cd1 has rank \(1\).

Complex multiplication

The elliptic curves in class 297825cd do not have complex multiplication.

Modular form 297825.2.a.cd

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