Cremona's table of elliptic curves

12615 = 3 · 5 · 29²

Field	Data	Notes
Atkin-Lehner	3- 5- 29+	Signs for the Atkin-Lehner involutions
Class	12615f	Isogeny class
Conductor	12615	Conductor
∏ cp	64	Product of Tamagawa factors cp
Δ	30112930625625 = 34 · 54 · 296	Discriminant
Eigenvalues	1 3- 5-  0  4 -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-8428,-138427]	[a1,a2,a3,a4,a6]
Generators	[-81:160:1]	Generators of the group modulo torsion
j	111284641/50625	j-invariant
L	7.237290736105	L(r)(E,1)/r!
Ω	0.52017091119552	Real period
R	3.4783234607791	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	37845d3 63075c3 15a1	Quadratic twists by: -3 5 29

Hecke Eigenvalues for elliptic curve 12615f3

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

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Quadratic twists for elliptic curve 12615f3

-3	5	29
37845d3	63075c3	15a1

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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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