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	3234o	Isogeny class
Conductor	3234	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	1078405366100832 = 25 · 312 · 78 · 11	Discriminant
Eigenvalues	2+ 3- -2 7- 11- -2 -6  8	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-4508222,-3684683824]	[a1,a2,a3,a4,a6]
j	86129359107301290313/9166294368	j-invariant
L	1.2433101855684	L(r)(E,1)/r!
Ω	0.1036091821307	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25872bo4 103488s4 9702bv3 80850ek4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234o3

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	-6	8	4	2	-8	6	-6	8	-4	10	-4	14	-4	-4	14	-8	-4	14	-18

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Quadratic twists for elliptic curve 3234o3

-4	8	-3	5	-7	-11
25872bo4	103488s4	9702bv3	80850ek4	462b3	35574de4

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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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