Cremona's table of elliptic curves

12320 = 2⁵ · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 5- 7+ 11+	Signs for the Atkin-Lehner involutions
Class	12320b	Isogeny class
Conductor	12320	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	332024000000 = 29 · 56 · 73 · 112	Discriminant
Eigenvalues	2+  2 5- 7+ 11+ -2 -2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-3200,65000]	[a1,a2,a3,a4,a6]
j	7080100070408/648484375	j-invariant
L	2.8124049886555	L(r)(E,1)/r!
Ω	0.93746832955184	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	12320n2 24640h2 110880cz2 61600bn2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320b2

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

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Quadratic twists for elliptic curve 12320b2

-4	8	-3	5	-7
12320n2	24640h2	110880cz2	61600bn2	86240c2

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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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