Properties

Label 100010.g
Number of curves $1$
Conductor $100010$
CM no
Rank $0$

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

Elliptic curves in class 100010.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100010.g1 100010i1 \([1, 0, 0, -111496565, -453157570783]\) \(153288006309736388746325476561/4114576216480000000\) \(4114576216480000000\) \([]\) \(9624384\) \(3.0852\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100010.g1 has rank \(0\).

Complex multiplication

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

Modular form 100010.2.a.g

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