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	12400r	Isogeny class
Conductor	12400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	118210688000000 = 213 · 56 · 314	Discriminant
Eigenvalues	2-  0 5+  0  0 -2  6 -4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-12275,19250]	[a1,a2,a3,a4,a6]
Generators	[-14:434:1]	Generators of the group modulo torsion
j	3196010817/1847042	j-invariant
L	4.3941895033552	L(r)(E,1)/r!
Ω	0.50067984394391	Real period
R	2.1941114449214	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	1550a3 49600bw3 111600ep3 496f4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400r4

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

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Quadratic twists for elliptic curve 12400r4

-4	8	-3	5
1550a3	49600bw3	111600ep3	496f4

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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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