Properties

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

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Show commands: SageMath
E = EllipticCurve("w1")
 
E.isogeny_class()
 

Elliptic curves in class 392784w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.w1 392784w1 \([0, -1, 0, -353030120, -2552911750416]\) \(29438568388080309583/779351913642\) \(128817810791658318618624\) \([]\) \(88058880\) \(3.5398\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784w1 has rank \(2\).

Complex multiplication

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

Modular form 392784.2.a.w

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 6 q^{11} - 4 q^{13} - q^{15} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display