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	12400q	Isogeny class
Conductor	12400	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	19681280000000 = 218 · 57 · 312	Discriminant
Eigenvalues	2- -2 5+ -4  0  4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-682408,-217204812]	[a1,a2,a3,a4,a6]
j	549131937598369/307520	j-invariant
L	0.6644288478672	L(r)(E,1)/r!
Ω	0.1661072119668	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1550d2 49600bt2 111600el2 2480i2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 12400q2

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	+	-4	0	4	0	4	-6	6	+	-8	-6	-10	0	0	12	14	8	0	4	-8	6	-18	10

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Quadratic twists for elliptic curve 12400q2

-4	8	-3	5
1550d2	49600bt2	111600el2	2480i2

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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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