Properties

Label 6762i
Number of curves $1$
Conductor $6762$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 6762i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6762.j1 6762i1 \([1, 1, 0, -81, -363]\) \(-174676879/35328\) \(-12117504\) \([]\) \(2880\) \(0.081691\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6762i1 has rank \(1\).

Complex multiplication

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

Modular form 6762.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{8} + q^{9} - 3 q^{10} + 2 q^{11} - q^{12} - 7 q^{13} - 3 q^{15} + q^{16} + 4 q^{17} - q^{18} - 6 q^{19} + O(q^{20})\) Copy content Toggle raw display