Cremona's table of elliptic curves

12600 = 2³ · 3² · 5² · 7

Field	Data	Notes
Atkin-Lehner	2+ 3- 5+ 7+	Signs for the Atkin-Lehner involutions
Class	12600o	Isogeny class
Conductor	12600	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-165337200 = -1 · 24 · 310 · 52 · 7	Discriminant
Eigenvalues	2+ 3- 5+ 7+  3  2  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-255,-1685]	[a1,a2,a3,a4,a6]
j	-6288640/567	j-invariant
L	2.3772163964308	L(r)(E,1)/r!
Ω	0.59430409910769	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	25200bq1 100800du1 4200y1 12600cn1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12600o1

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

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Quadratic twists for elliptic curve 12600o1

-4	8	-3	5	-7
25200bq1	100800du1	4200y1	12600cn1	88200ck1

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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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