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	12320d	Isogeny class
Conductor	12320	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	166960640000 = 212 · 54 · 72 · 113	Discriminant
Eigenvalues	2+  2 5- 7- 11+ -4 -8  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-6865,-215775]	[a1,a2,a3,a4,a6]
Generators	[135:1140:1]	Generators of the group modulo torsion
j	8736724668736/40761875	j-invariant
L	6.9384375723688	L(r)(E,1)/r!
Ω	0.52463357694482	Real period
R	3.306325537137	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	12320i2 24640q1 110880dh2 61600be2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12320d2

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	-8	8	4	-2	2	-6	-12	4	-6	-6	6	-12	-4	16	4	0	-16	-6	-18

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Quadratic twists for elliptic curve 12320d2

-4	8	-3	5	-7
12320i2	24640q1	110880dh2	61600be2	86240d2

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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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