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	18	Product of Tamagawa factors cp
deg	144	Modular degree for the optimal curve
Δ	-33958656 = -1 · 28 · 33 · 173	Discriminant
Eigenvalues	2- 3+ -3  2 -3 -1 17- -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-24,-284]	[a1,a2,a3,a4,a6]
Generators	[8:6:1]	Generators of the group modulo torsion
j	-221184/4913	j-invariant
L	1.9203816973899	L(r)(E,1)/r!
Ω	0.89472316921524	Real period
R	1.0731708775767	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	3	Number of elements in the torsion subgroup
Twists	2448l1 9792f1 612a2 15300c1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 612b1

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 612b1

-4	8	-3	5	-7	-11	13	17
2448l1	9792f1	612a2	15300c1	29988k1	74052a1	103428f1	10404d1

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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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