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	30576bs	Isogeny class
Conductor	30576	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	41289806917632 = 212 · 3 · 76 · 134	Discriminant
Eigenvalues	2- 3+ -2 7- -4 13+ -2  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-15304,665008]	[a1,a2,a3,a4,a6]
Generators	[138:1078:1]	Generators of the group modulo torsion
j	822656953/85683	j-invariant
L	2.9372847426365	L(r)(E,1)/r!
Ω	0.62491727564579	Real period
R	2.3501388560597	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	1911f3 122304ig3 91728ef3 624h3	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576bs3

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

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Quadratic twists for elliptic curve 30576bs3

-4	8	-3	-7
1911f3	122304ig3	91728ef3	624h3

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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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