Properties

Label 6776b
Number of curves $1$
Conductor $6776$
CM no
Rank $2$

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Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 6776b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6776.b1 6776b1 \([0, 0, 0, -1804, 29524]\) \(-1905527808/2401\) \(-818107136\) \([]\) \(9984\) \(0.61888\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6776b1 has rank \(2\).

Complex multiplication

The elliptic curves in class 6776b do not have complex multiplication.

Modular form 6776.2.a.b

sage: E.q_eigenform(10)
 
\(q - 3 q^{3} - 3 q^{5} + q^{7} + 6 q^{9} - 4 q^{13} + 9 q^{15} - 4 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display