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	6300a	Isogeny class
Conductor	6300	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	6912	Modular degree for the optimal curve
Δ	57881250000 = 24 · 33 · 58 · 73	Discriminant
Eigenvalues	2- 3+ 5+ 7+  0  4  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-8700,312125]	[a1,a2,a3,a4,a6]
j	10788913152/8575	j-invariant
L	2.2100370885151	L(r)(E,1)/r!
Ω	1.1050185442575	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	25200cy1 100800g1 6300b3 1260b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 6300a1

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

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Quadratic twists for elliptic curve 6300a1

-4	8	-3	5	-7
25200cy1	100800g1	6300b3	1260b1	44100h1

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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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