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	30576cs	Isogeny class
Conductor	30576	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-5812559241216 = -1 · 213 · 3 · 72 · 136	Discriminant
Eigenvalues	2- 3- -3 7- -3 13+ -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,3008,-96076]	[a1,a2,a3,a4,a6]
Generators	[1830:17576:27] [178:2472:1]	Generators of the group modulo torsion
j	14991903983/28960854	j-invariant
L	8.2833374649987	L(r)(E,1)/r!
Ω	0.39610513366054	Real period
R	2.6139958691177	Regulator
r	2	Rank of the group of rational points
S	0.99999999999986	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	3822t2 122304gk2 91728eo2 30576bl2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576cs2

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
-	-	-3	-	-3	+	-6	-4	-6	-9	5	-4	12	4	-12	-9	-9	-8	4	-6	-14	1	3	0	-5

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Quadratic twists for elliptic curve 30576cs2

-4	8	-3	-7
3822t2	122304gk2	91728eo2	30576bl2

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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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