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	8	Product of Tamagawa factors cp
Δ	62000000000 = 210 · 59 · 31	Discriminant
Eigenvalues	2+  0 5+  0  4 -2 -6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2066675,1143553250]	[a1,a2,a3,a4,a6]
Generators	[19136090:2639893773:1000]	Generators of the group modulo torsion
j	61012706050976004/3875	j-invariant
L	4.3959588387284	L(r)(E,1)/r!
Ω	0.60897215446845	Real period
R	14.437306554896	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	6200e3 49600bk4 111600w4 2480e3	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400b3

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 12400b3

-4	8	-3	5
6200e3	49600bk4	111600w4	2480e3

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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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