Cremona's table of elliptic curves

3108 = 2² · 3 · 7 · 37

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 37-	Signs for the Atkin-Lehner involutions
Class	3108b	Isogeny class
Conductor	3108	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	576	Modular degree for the optimal curve
Δ	2349648 = 24 · 34 · 72 · 37	Discriminant
Eigenvalues	2- 3+  0 7+  0  4 -8  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-33,18]	[a1,a2,a3,a4,a6]
Generators	[-3:9:1]	Generators of the group modulo torsion
j	256000000/146853	j-invariant
L	2.8712295450023	L(r)(E,1)/r!
Ω	2.2108243929505	Real period
R	0.43290481055507	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	12432bw1 49728bh1 9324c1 77700v1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3108b1

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
-	+	0	+	0	4	-8	8	-6	2	-8	-	2	10	8	-10	-8	0	12	12	-6	-10	-12	-8	-16

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Quadratic twists for elliptic curve 3108b1

-4	8	-3	5	-7	37
12432bw1	49728bh1	9324c1	77700v1	21756o1	114996a1

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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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