Properties

Label 6762.be
Number of curves $1$
Conductor $6762$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 6762.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.be1 6762bc1 \([1, 1, 1, 568301, 291869969]\) \(503009937352889/1201583849472\) \(-48488242439140245504\) \([]\) \(262080\) \(2.4613\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6762.be1 has rank \(0\).

Complex multiplication

The elliptic curves in class 6762.be do not have complex multiplication.

Modular form 6762.2.a.be

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + 3q^{5} - q^{6} + q^{8} + q^{9} + 3q^{10} + 2q^{11} - q^{12} + 5q^{13} - 3q^{15} + q^{16} + 4q^{17} + q^{18} - 6q^{19} + O(q^{20})\)  Toggle raw display