Cremona's table of elliptic curves

6300 = 2² · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	6300f	Isogeny class
Conductor	6300	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	-42185786580000000 = -1 · 28 · 316 · 57 · 72	Discriminant
Eigenvalues	2- 3- 5+ 7+  2 -4  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-121575,-19075250]	[a1,a2,a3,a4,a6]
Generators	[71830:1255086:125]	Generators of the group modulo torsion
j	-68150496976/14467005	j-invariant
L	3.9489115747395	L(r)(E,1)/r!
Ω	0.12640046408722	Real period
R	7.810318583986	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	25200ek2 100800dl2 2100k2 1260f2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300f2

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

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Quadratic twists for elliptic curve 6300f2

-4	8	-3	5	-7
25200ek2	100800dl2	2100k2	1260f2	44100bp2

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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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