Properties

Label 3822.bf
Number of curves $1$
Conductor $3822$
CM no
Rank $1$

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

Elliptic curves in class 3822.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
3822.bf1 3822bf1 \([1, 0, 0, -78, 468]\) \(-1071912625/1364688\) \(-66869712\) \([]\) \(1536\) \(0.19473\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 3822.bf1 has rank \(1\).

Complex multiplication

The elliptic curves in class 3822.bf do not have complex multiplication.

Modular form 3822.2.a.bf

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 5 q^{11} + q^{12} + q^{13} + q^{16} - 7 q^{17} + q^{18} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display