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	30576w	Isogeny class
Conductor	30576	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	4698430464 = 210 · 3 · 76 · 13	Discriminant
Eigenvalues	2+ 3- -2 7-  0 13+ -2 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-40784,-3183804]	[a1,a2,a3,a4,a6]
Generators	[-1245618:-9465:10648]	Generators of the group modulo torsion
j	62275269892/39	j-invariant
L	5.4612019352472	L(r)(E,1)/r!
Ω	0.33595122504486	Real period
R	8.1279684789332	Regulator
r	1	Rank of the group of rational points
S	0.99999999999999	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	15288v3 122304ga4 91728w4 624c3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576w4

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	-	0	+	-2	-4	0	6	0	-2	-6	12	-4	6	-8	2	-4	12	14	0	8	18	6

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Quadratic twists for elliptic curve 30576w4

-4	8	-3	-7
15288v3	122304ga4	91728w4	624c3

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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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