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	30576bw	Isogeny class
Conductor	30576	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	17280	Modular degree for the optimal curve
Δ	220238928 = 24 · 32 · 76 · 13	Discriminant
Eigenvalues	2- 3+  4 7-  4 13+ -2 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-261,1548]	[a1,a2,a3,a4,a6]
Generators	[-54:435:8]	Generators of the group modulo torsion
j	1048576/117	j-invariant
L	6.6523899719799	L(r)(E,1)/r!
Ω	1.7152936319162	Real period
R	3.8782805743576	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	7644g1 122304it1 91728ev1 624j1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 30576bw1

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
-	+	4	-	4	+	-2	-2	0	-6	-10	10	-8	-4	-4	-10	-8	14	-2	-16	10	16	0	4	2

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Quadratic twists for elliptic curve 30576bw1

-4	8	-3	-7
7644g1	122304it1	91728ev1	624j1

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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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