Properties

Label 297825.j
Number of curves $1$
Conductor $297825$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 297825.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
297825.j1 297825j1 \([1, 1, 1, 189337, 444682406]\) \(2828663/323433\) \(-85828824141246140625\) \([]\) \(10506240\) \(2.5043\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 297825.j1 has rank \(1\).

Complex multiplication

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

Modular form 297825.2.a.j

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