Cremona's table of elliptic curves

612 = 2² · 3² · 17

Field	Data	Notes
Atkin-Lehner	2- 3+ 17+	Signs for the Atkin-Lehner involutions
Class	612a	Isogeny class
Conductor	612	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-24755860224 = -1 · 28 · 39 · 173	Discriminant
Eigenvalues	2- 3+  3  2  3 -1 17+ -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-216,7668]	[a1,a2,a3,a4,a6]
j	-221184/4913	j-invariant
L	2.0067849520135	L(r)(E,1)/r!
Ω	1.0033924760068	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2448j2 9792c2 612b1 15300g2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 612a2

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
-	+	3	2	3	-1	+	-7	3	6	-4	2	9	-1	-12	12	-6	2	-4	0	8	14	-12	-6	-16

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Quadratic twists for elliptic curve 612a2

-4	8	-3	5	-7	-11	13	17
2448j2	9792c2	612b1	15300g2	29988q2	74052b2	103428c2	10404e2

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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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