Properties

Label 397488.dj
Number of curves $1$
Conductor $397488$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("dj1")
 
E.isogeny_class()
 

Elliptic curves in class 397488.dj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
397488.dj1 397488dj1 \([0, -1, 0, 328480, 163610784]\) \(68782/243\) \(-13847796088938878976\) \([]\) \(7257600\) \(2.3559\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 397488.dj1 has rank \(1\).

Complex multiplication

The elliptic curves in class 397488.dj do not have complex multiplication.

Modular form 397488.2.a.dj

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + 3 q^{11} - q^{15} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display