Cremona's table of elliptic curves

21156 = 2² · 3 · 41 · 43

Field	Data	Notes
Atkin-Lehner	2- 3- 41- 43-	Signs for the Atkin-Lehner involutions
Class	21156f	Isogeny class
Conductor	21156	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	28224	Modular degree for the optimal curve
Δ	-61453271808 = -1 · 28 · 34 · 413 · 43	Discriminant
Eigenvalues	2- 3- -4  1  2 -4 -2 -1	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-1445,23799]	[a1,a2,a3,a4,a6]
Generators	[34:123:1]	Generators of the group modulo torsion
j	-1304330960896/240051843	j-invariant
L	4.7213524280719	L(r)(E,1)/r!
Ω	1.0643968149122	Real period
R	0.36964225198767	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	84624o1 63468e1	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 21156f1

a2	a3	a5	a7	a11	a13	a17	a19	a23	a29	a31	a37	a41	a43	a47	a53	a59	a61	a67	a71	a73	a79	a83	a89	a97
-	-	-4	1	2	-4	-2	-1	8	7	-7	-2	-	-	-4	-12	-5	-8	-2	12	16	16	-7	-9	2

---

Quadratic twists for elliptic curve 21156f1

-4	-3
84624o1	63468e1

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations