Properties

Label 100011.c
Number of curves $1$
Conductor $100011$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("c1")
 
E.isogeny_class()
 

Elliptic curves in class 100011.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100011.c1 100011a1 \([1, 1, 1, 35551, 4633994]\) \(4969107733387776623/12093154029532179\) \(-12093154029532179\) \([]\) \(766224\) \(1.7698\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100011.c1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100011.c do not have complex multiplication.

Modular form 100011.2.a.c

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