Cremona's table of elliptic curves

468 = 2² · 3² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	468c	Isogeny class
Conductor	468	Conductor
∏ cp	12	Product of Tamagawa factors cp
Δ	-31539456 = -1 · 28 · 36 · 132	Discriminant
Eigenvalues	2- 3- -2 -2  2 13+ -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,9,270]	[a1,a2,a3,a4,a6]
Generators	[3:18:1]	Generators of the group modulo torsion
j	432/169	j-invariant
L	1.7484928207284	L(r)(E,1)/r!
Ω	1.6179172250757	Real period
R	0.36023532675817	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	1872o2 7488bb2 52a1 11700o2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 468c2

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	-6	-8	-2	10	-6	6	4	2	-6	10	-2	10	-10	2	-4	6	6	2

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Quadratic twists for elliptic curve 468c2

-4	8	-3	5	-7	-11	13
1872o2	7488bb2	52a1	11700o2	22932w2	56628z2	6084i2

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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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