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	612b	Isogeny class
Conductor	612	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	-85660416 = -1 · 28 · 39 · 17	Discriminant
Eigenvalues	2- 3+ -3  2 -3 -1 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-4104,-101196]	[a1,a2,a3,a4,a6]
Generators	[93:567:1]	Generators of the group modulo torsion
j	-1517101056/17	j-invariant
L	1.9203816973899	L(r)(E,1)/r!
Ω	0.29824105640508	Real period
R	3.2195126327301	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	2448l2 9792f2 612a1 15300c2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 612b2

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 612b2

-4	8	-3	5	-7	-11	13	17
2448l2	9792f2	612a1	15300c2	29988k2	74052a2	103428f2	10404d2

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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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