Properties

Label 100010g
Number of curves $1$
Conductor $100010$
CM no
Rank $1$

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

Elliptic curves in class 100010g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100010.k1 100010g1 \([1, -1, 1, -62577, 6040609]\) \(27099508997725670241/897932984320\) \(897932984320\) \([]\) \(980832\) \(1.3868\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100010g1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100010g do not have complex multiplication.

Modular form 100010.2.a.g

sage: E.q_eigenform(10)
 
\(q + q^{2} + 3 q^{3} + q^{4} + q^{5} + 3 q^{6} + 3 q^{7} + q^{8} + 6 q^{9} + q^{10} + q^{11} + 3 q^{12} - 6 q^{13} + 3 q^{14} + 3 q^{15} + q^{16} - 2 q^{17} + 6 q^{18} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display