Properties

Label 106722.gr
Number of curves $1$
Conductor $106722$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("gr1")
 
E.isogeny_class()
 

Elliptic curves in class 106722.gr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
106722.gr1 106722ef1 \([1, -1, 1, -29545319, 61836728671]\) \(-34068278205171/10307264\) \(-862944695036146400832\) \([]\) \(7257600\) \(2.9948\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 106722.gr1 has rank \(1\).

Complex multiplication

The elliptic curves in class 106722.gr do not have complex multiplication.

Modular form 106722.2.a.gr

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