Cremona's table of elliptic curves

231 = 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	3+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	231a	Isogeny class
Conductor	231	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-13504609503 = -1 · 32 · 7 · 118	Discriminant
Eigenvalues	-1 3+ -2 7- 11+  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,31,-5578]	[a1,a2,a3,a4,a6]
j	3288008303/13504609503	j-invariant
L	0.5822888619653	L(r)(E,1)/r!
Ω	0.5822888619653	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	3696w6 14784bm6 693d6 5775n6	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 231a6

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
-1	+	-2	-	+	6	2	4	0	-2	8	6	10	-4	-8	6	4	-10	-12	0	2	16	4	18	2

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Quadratic twists for elliptic curve 231a6

-4	8	-3	5	-7	-11	13	17	-19	-23
3696w6	14784bm6	693d6	5775n6	1617g6	2541b6	39039h5	66759g5	83391r5	122199f5

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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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