Properties

Label 214371643.a
Number of curves $1$
Conductor $214371643$
CM no
Rank $5$

Related objects

Downloads

Learn more

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

Elliptic curves in class 214371643.a

sage: E.isogeny_class().curves
 
LMFDB label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height
214371643.a1 \([0, 1, 1, -100, 770]\) \(-111701610496/214371643\) \(-214371643\) \([]\) \(\) \(0.28831\)

Rank

sage: E.rank()
 

The elliptic curve 214371643.a1 has rank \(5\).

Complex multiplication

The elliptic curves in class 214371643.a do not have complex multiplication.

Modular form 214371643.2.a.a

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