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	12400x	Isogeny class
Conductor	12400	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	12300800000000 = 215 · 58 · 312	Discriminant
Eigenvalues	2-  2 5+  0 -2  0 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-426408,107315312]	[a1,a2,a3,a4,a6]
Generators	[-739:4278:1]	Generators of the group modulo torsion
j	133974081659809/192200	j-invariant
L	6.4220766991176	L(r)(E,1)/r!
Ω	0.60546874084856	Real period
R	5.3033924510431	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	1550c2 49600ci2 111600er2 2480l2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400x2

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
-	2	+	0	-2	0	-2	4	-4	-4	-	8	6	2	0	-8	-8	0	4	0	-6	4	6	-6	2

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Quadratic twists for elliptic curve 12400x2

-4	8	-3	5
1550c2	49600ci2	111600er2	2480l2

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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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