Cremona's table of elliptic curves

19600 = 2⁴ · 5² · 7²

Field	Data	Notes
Atkin-Lehner	2- 5- 7+	Signs for the Atkin-Lehner involutions
Class	19600dg	Isogeny class
Conductor	19600	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-46118408000000000 = -1 · 212 · 59 · 78	Discriminant
Eigenvalues	2-  1 5- 7+  0  2  2 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-4078427208,-100252007070412]	[a1,a2,a3,a4,a6]
Generators	[450719126720791190776308886489985301621406420423223224102834554737202330102307388322145528790838683012:-174269584212283143023792073659452662049863416424717370847374107478455734969365663590396181320974210426750:2562089016583017268431996395045593599526501648178393070664058858733691359578005081799983181872139]	Generators of the group modulo torsion
j	-162677523113838677	j-invariant
L	5.9378634124386	L(r)(E,1)/r!
Ω	0.0094459660461144	Real period
R	157.15341828063	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	1225e2 78400jn2 19600dh2 19600dv2	Quadratic twists by: -4 8 5 -7

Hecke Eigenvalues for elliptic curve 19600dg2

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
-	1	-	+	0	2	2	-6	3	7	-2	-8	5	-7	0	6	-10	7	5	2	-6	2	11	9	-16

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Quadratic twists for elliptic curve 19600dg2

-4	8	5	-7
1225e2	78400jn2	19600dh2	19600dv2

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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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