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	16	Product of Tamagawa factors cp
deg	27648	Modular degree for the optimal curve
Δ	-79360000000000 = -1 · 218 · 510 · 31	Discriminant
Eigenvalues	2-  2 5+  0 -2  0 -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-26408,1715312]	[a1,a2,a3,a4,a6]
Generators	[746:1875:8]	Generators of the group modulo torsion
j	-31824875809/1240000	j-invariant
L	6.4220766991176	L(r)(E,1)/r!
Ω	0.60546874084856	Real period
R	2.6516962255215	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	1550c1 49600ci1 111600er1 2480l1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400x1

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 12400x1

-4	8	-3	5
1550c1	49600ci1	111600er1	2480l1

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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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