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	3234s	Isogeny class
Conductor	3234	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	227369869188 = 22 · 3 · 76 · 115	Discriminant
Eigenvalues	2- 3+  4 7- 11- -4  2  0	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-493186,133104971]	[a1,a2,a3,a4,a6]
j	112763292123580561/1932612	j-invariant
L	3.5539228549336	L(r)(E,1)/r!
Ω	0.71078457098671	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	25872cs3 103488do3 9702t3 80850cp3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3234s3

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

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Quadratic twists for elliptic curve 3234s3

-4	8	-3	5	-7	-11
25872cs3	103488do3	9702t3	80850cp3	66c3	35574q3

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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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