Cremona's table of elliptic curves

3627 = 3² · 13 · 31

Field	Data	Notes
Atkin-Lehner	3- 13- 31+	Signs for the Atkin-Lehner involutions
Class	3627b	Isogeny class
Conductor	3627	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	-16671263249043 = -1 · 316 · 13 · 313	Discriminant
Eigenvalues	2 3- -2  2 -1 13- -8  6	Hecke eigenvalues for primes up to 20
Equation	[0,0,1,-3981,218947]	[a1,a2,a3,a4,a6]
Generators	[-382:4379:8]	Generators of the group modulo torsion
j	-9571339399168/22868673867	j-invariant
L	6.1658493692785	L(r)(E,1)/r!
Ω	0.61514657896884	Real period
R	5.0116911806729	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	58032bp1 1209a1 90675t1 47151d1	Quadratic twists by: -4 -3 5 13

Hecke Eigenvalues for elliptic curve 3627b1

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	2	-1	-	-8	6	-6	4	+	-5	-6	-6	0	12	6	-2	-8	-12	11	8	-4	-13	-14

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Quadratic twists for elliptic curve 3627b1

-4	-3	5	13	-31
58032bp1	1209a1	90675t1	47151d1	112437i1

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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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