Cremona's table of elliptic curves

30192 = 2⁴ · 3 · 17 · 37

Field	Data	Notes
Atkin-Lehner	2+ 3- 17- 37+	Signs for the Atkin-Lehner involutions
Class	30192i	Isogeny class
Conductor	30192	Conductor
∏ cp	128	Product of Tamagawa factors cp
Δ	3638938647315456 = 210 · 38 · 172 · 374	Discriminant
Eigenvalues	2+ 3-  2 -4  4 -2 17-  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-628392,-191919420]	[a1,a2,a3,a4,a6]
Generators	[990:12540:1]	Generators of the group modulo torsion
j	26798864258584160932/3553651022769	j-invariant
L	7.1584081542054	L(r)(E,1)/r!
Ω	0.16956854390826	Real period
R	5.2769281297822	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	15096f2 120768ct2 90576d2	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 30192i2

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	4	-2	-	4	-4	-6	4	+	2	4	-8	-2	-12	2	-4	12	-6	4	-12	-6	2

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Quadratic twists for elliptic curve 30192i2

-4	8	-3
15096f2	120768ct2	90576d2

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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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