Properties

Label 392784d
Number of curves $1$
Conductor $392784$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("d1")
 
E.isogeny_class()
 

Elliptic curves in class 392784d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.d1 392784d1 \([0, -1, 0, -238352, 44869056]\) \(-7461495947842657/192384\) \(-38612238336\) \([]\) \(1806336\) \(1.5473\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784d1 has rank \(2\).

Complex multiplication

The elliptic curves in class 392784d do not have complex multiplication.

Modular form 392784.2.a.d

sage: E.q_eigenform(10)
 
\(q - q^{3} - 3 q^{5} + q^{9} + q^{13} + 3 q^{15} - 2 q^{17} + 2 q^{19} + O(q^{20})\) Copy content Toggle raw display