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	3234f	Isogeny class
Conductor	3234	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-6623232 = -1 · 212 · 3 · 72 · 11	Discriminant
Eigenvalues	2+ 3+  0 7- 11-  4 -3  1	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-5835,169149]	[a1,a2,a3,a4,a6]
Generators	[38:45:1]	Generators of the group modulo torsion
j	-448504189023625/135168	j-invariant
L	2.2382146448734	L(r)(E,1)/r!
Ω	1.9058693793107	Real period
R	0.58718993787574	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	25872cj2 103488cv2 9702bs2 80850gs2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234f2

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
+	+	0	-	-	4	-3	1	-3	-9	-2	-7	6	11	3	0	-9	10	-4	3	4	-16	0	0	1

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Quadratic twists for elliptic curve 3234f2

-4	8	-3	5	-7	-11
25872cj2	103488cv2	9702bs2	80850gs2	3234j2	35574bx2

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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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