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	3234t	Isogeny class
Conductor	3234	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	7764834 = 2 · 3 · 76 · 11	Discriminant
Eigenvalues	2- 3- -2 7- 11+  6 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-17249,870519]	[a1,a2,a3,a4,a6]
j	4824238966273/66	j-invariant
L	3.3171064896445	L(r)(E,1)/r!
Ω	1.6585532448223	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872by4 103488by4 9702x3 80850o4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234t3

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

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Quadratic twists for elliptic curve 3234t3

-4	8	-3	5	-7	-11
25872by4	103488by4	9702x3	80850o4	66b3	35574bk4

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

Part of Computational Number Theory
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