Cremona's table of elliptic curves

12400 = 2⁴ · 5² · 31

Field	Data	Notes
Atkin-Lehner	2+ 5+ 31+	Signs for the Atkin-Lehner involutions
Class	12400b	Isogeny class
Conductor	12400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	60062500000000 = 28 · 512 · 312	Discriminant
Eigenvalues	2+  0 5+  0  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-129175,17865750]	[a1,a2,a3,a4,a6]
Generators	[152930:21140625:8]	Generators of the group modulo torsion
j	59593532744016/15015625	j-invariant
L	4.3959588387284	L(r)(E,1)/r!
Ω	0.60897215446845	Real period
R	7.2186532774482	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	6200e2 49600bk2 111600w2 2480e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400b2

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

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Quadratic twists for elliptic curve 12400b2

-4	8	-3	5
6200e2	49600bk2	111600w2	2480e2

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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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