Cremona's table of elliptic curves

3234 = 2 · 3 · 7² · 11

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	3234r	Isogeny class
Conductor	3234	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	5824720341594 = 2 · 38 · 79 · 11	Discriminant
Eigenvalues	2- 3+ -2 7- 11-  2  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-1972104,-1066786449]	[a1,a2,a3,a4,a6]
j	7209828390823479793/49509306	j-invariant
L	2.0383890743779	L(r)(E,1)/r!
Ω	0.12739931714862	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872co4 103488dd4 9702p4 80850ck4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234r3

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
-	+	-2	-	-	2	2	0	0	-2	-4	-2	10	4	-4	-2	12	2	12	8	-6	-8	8	14	14

---

Quadratic twists for elliptic curve 3234r3

-4	8	-3	5	-7	-11
25872co4	103488dd4	9702p4	80850ck4	462f4	35574o4

---

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