Cremona's table of elliptic curves

21315 = 3 · 5 · 7² · 29

Field	Data	Notes
Atkin-Lehner	3+ 5+ 7- 29-	Signs for the Atkin-Lehner involutions
Class	21315f	Isogeny class
Conductor	21315	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-468061325825625 = -1 · 32 · 54 · 76 · 294	Discriminant
Eigenvalues	-1 3+ 5+ 7-  0 -6 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-19111,1447214]	[a1,a2,a3,a4,a6]
Generators	[14:1080:1]	Generators of the group modulo torsion
j	-6561258219361/3978455625	j-invariant
L	1.6051638577444	L(r)(E,1)/r!
Ω	0.48709976711695	Real period
R	0.41191865766151	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	63945y3 106575cb3 435d4	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 21315f3

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	-6	-2	-8	-4	-	-4	6	-2	-4	0	6	12	-6	-8	16	6	12	16	-2	14

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Quadratic twists for elliptic curve 21315f3

-3	5	-7
63945y3	106575cb3	435d4

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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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