Cremona's table of elliptic curves

30912 = 2⁶ · 3 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 23+	Signs for the Atkin-Lehner involutions
Class	30912bn	Isogeny class
Conductor	30912	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	8599965696 = 212 · 34 · 72 · 232	Discriminant
Eigenvalues	2- 3+  2 7- -4  2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-537,-1575]	[a1,a2,a3,a4,a6]
Generators	[29:80:1]	Generators of the group modulo torsion
j	4188852928/2099601	j-invariant
L	5.532742717446	L(r)(E,1)/r!
Ω	1.0447952906076	Real period
R	2.6477640008449	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	30912ca2 15456t1 92736fp2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 30912bn2

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

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Quadratic twists for elliptic curve 30912bn2

-4	8	-3
30912ca2	15456t1	92736fp2

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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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