Properties

Label 666.g
Number of curves $1$
Conductor $666$
CM no
Rank $0$

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 666.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
666.g1 666g1 \([1, -1, 1, -1640858, -808607271]\) \(-670206957616537490521/6109179936768\) \(-4453592173903872\) \([]\) \(19872\) \(2.1673\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 666.g1 has rank \(0\).

Complex multiplication

The elliptic curves in class 666.g do not have complex multiplication.

Modular form 666.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + 4 q^{5} + 3 q^{7} + q^{8} + 4 q^{10} - 5 q^{11} + 3 q^{13} + 3 q^{14} + q^{16} - 3 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display