Cremona's table of elliptic curves

8680 = 2³ · 5 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 5+ 7+ 31+	Signs for the Atkin-Lehner involutions
Class	8680k	Isogeny class
Conductor	8680	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	497002061360000000 = 210 · 57 · 7 · 316	Discriminant
Eigenvalues	2- -2 5+ 7+  2  6 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-11656736,-15322253936]	[a1,a2,a3,a4,a6]
j	171062444945787531357316/485353575546875	j-invariant
L	1.3073003214753	L(r)(E,1)/r!
Ω	0.081706270092209	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	16	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	17360i2 69440bg2 78120n2 43400g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 8680k2

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

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Quadratic twists for elliptic curve 8680k2

-4	8	-3	5	-7
17360i2	69440bg2	78120n2	43400g2	60760y2

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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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