Properties

Label 100027.a
Number of curves $1$
Conductor $100027$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 100027.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
100027.a1 100027a1 \([1, -1, 1, 2, -16]\) \(1367631/100027\) \(-100027\) \([]\) \(14088\) \(-0.36102\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 100027.a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 100027.a do not have complex multiplication.

Modular form 100027.2.a.a

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