Cremona's table of elliptic curves

30576 = 2⁴ · 3 · 7² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3- 7- 13+	Signs for the Atkin-Lehner involutions
Class	30576v	Isogeny class
Conductor	30576	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-4127473613810706432 = -1 · 211 · 3 · 77 · 138	Discriminant
Eigenvalues	2+ 3-  2 7-  4 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-422592,-144136812]	[a1,a2,a3,a4,a6]
Generators	[328558855324228755:-9437207836960823374:262205444800125]	Generators of the group modulo torsion
j	-34639400027234/17130345141	j-invariant
L	8.2214695154789	L(r)(E,1)/r!
Ω	0.091474831273392	Real period
R	22.469212025402	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	15288u6 122304gh5 91728ba5 4368d6	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576v5

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

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Quadratic twists for elliptic curve 30576v5

-4	8	-3	-7
15288u6	122304gh5	91728ba5	4368d6

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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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