Cremona's table of elliptic curves

31680 = 2⁶ · 3² · 5 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3- 5- 11+	Signs for the Atkin-Lehner involutions
Class	31680bn	Isogeny class
Conductor	31680	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	31476810055680 = 216 · 38 · 5 · 114	Discriminant
Eigenvalues	2+ 3- 5- -4 11+ -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-36012,2616496]	[a1,a2,a3,a4,a6]
Generators	[125:261:1]	Generators of the group modulo torsion
j	108108036004/658845	j-invariant
L	4.3585786705272	L(r)(E,1)/r!
Ω	0.66233676592729	Real period
R	3.2903040377239	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	31680ed3 3960f4 10560x3	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31680bn3

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

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Quadratic twists for elliptic curve 31680bn3

-4	8	-3
31680ed3	3960f4	10560x3

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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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