Cremona's table of elliptic curves

3675 = 3 · 5² · 7²

Field	Data	Notes
Atkin-Lehner	3- 5+ 7-	Signs for the Atkin-Lehner involutions
Class	3675k	Isogeny class
Conductor	3675	Conductor
∏ cp	5	Product of Tamagawa factors cp
deg	360	Modular degree for the optimal curve
Δ	-297675 = -1 · 35 · 52 · 72	Discriminant
Eigenvalues	-1 3- 5+ 7-  0 -3  2 -1	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-8,27]	[a1,a2,a3,a4,a6]
Generators	[1:4:1]	Generators of the group modulo torsion
j	-46585/243	j-invariant
L	2.6765856771289	L(r)(E,1)/r!
Ω	2.6613609109158	Real period
R	0.20114413390161	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	58800fg1 11025w1 3675g1 3675b1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 3675k1

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
-1	-	+	-	0	-3	2	-1	-2	-8	8	-7	0	8	-10	14	-10	-7	5	-12	-11	-7	14	6	9

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Quadratic twists for elliptic curve 3675k1

-4	-3	5	-7
58800fg1	11025w1	3675g1	3675b1

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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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