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	2	Product of Tamagawa factors cp
deg	20	Modular degree for the optimal curve
Δ	1617 = 3 · 72 · 11	Discriminant
Eigenvalues	-1 3+ -2 7- 11+  6  2  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-34,62]	[a1,a2,a3,a4,a6]
j	4354703137/1617	j-invariant
L	0.5822888619653	L(r)(E,1)/r!
Ω	4.6583108957224	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3696w1 14784bm1 693d1 5775n1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 231a1

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 231a1

-4	8	-3	5	-7	-11	13	17	-19	-23
3696w1	14784bm1	693d1	5775n1	1617g1	2541b1	39039h1	66759g1	83391r1	122199f1

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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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