Cremona's table of elliptic curves

31920 = 2⁴ · 3 · 5 · 7 · 19

Field	Data	Notes
Atkin-Lehner	2- 3- 5- 7- 19+	Signs for the Atkin-Lehner involutions
Class	31920bx	Isogeny class
Conductor	31920	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-116868652682772480 = -1 · 216 · 3 · 5 · 7 · 198	Discriminant
Eigenvalues	2- 3- 5- 7- -4 -2  2 19+	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,99920,11112020]	[a1,a2,a3,a4,a6]
Generators	[3081:132308:27]	Generators of the group modulo torsion
j	26934982258902479/28532385908880	j-invariant
L	7.2798343013208	L(r)(E,1)/r!
Ω	0.21990128244717	Real period
R	8.2762526670005	Regulator
r	1	Rank of the group of rational points
S	4	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	3990u4 127680ee3 95760dm3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31920bx3

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	-2	2	+	0	6	0	-2	-6	-12	8	-10	4	14	-4	0	10	-8	-12	10	-14

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Quadratic twists for elliptic curve 31920bx3

-4	8	-3
3990u4	127680ee3	95760dm3

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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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