Properties

Label 392784.bf
Number of curves $1$
Conductor $392784$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 392784.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
392784.bf1 392784bf1 \([0, -1, 0, -44424, 3551472]\) \(6901323756319/147750912\) \(207579393294336\) \([]\) \(2350080\) \(1.5362\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 392784.bf1 has rank \(1\).

Complex multiplication

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

Modular form 392784.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{3} + 3 q^{5} + q^{9} - 6 q^{11} - 4 q^{13} - 3 q^{15} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display