Cremona's table of elliptic curves

3680 = 2⁵ · 5 · 23

Field	Data	Notes
Atkin-Lehner	2- 5+ 23-	Signs for the Atkin-Lehner involutions
Class	3680g	Isogeny class
Conductor	3680	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	704	Modular degree for the optimal curve
Δ	21160000 = 26 · 54 · 232	Discriminant
Eigenvalues	2-  0 5+  0  4 -2  2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-193,-1008]	[a1,a2,a3,a4,a6]
Generators	[1143:38640:1]	Generators of the group modulo torsion
j	12422690496/330625	j-invariant
L	3.2934143695729	L(r)(E,1)/r!
Ω	1.2829677237114	Real period
R	5.1340564672127	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	3680d1 7360y2 33120n1 18400a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3680g1

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

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Quadratic twists for elliptic curve 3680g1

-4	8	-3	5	-23
3680d1	7360y2	33120n1	18400a1	84640p1

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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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