Cremona's table of elliptic curves

12390 = 2 · 3 · 5 · 7 · 59

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 7+ 59-	Signs for the Atkin-Lehner involutions
Class	12390s	Isogeny class
Conductor	12390	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	4507763713040700 = 22 · 312 · 52 · 7 · 594	Discriminant
Eigenvalues	2- 3- 5+ 7+  4 -6  6 -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-56601,-4058019]	[a1,a2,a3,a4,a6]
j	20053791912530508049/4507763713040700	j-invariant
L	3.7740447028816	L(r)(E,1)/r!
Ω	0.31450372524013	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	99120bo3 37170k3 61950g3 86730cd3	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 12390s4

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
-	-	+	+	4	-6	6	-4	-8	6	0	6	-2	8	0	-2	-	10	8	-4	-2	8	4	-14	6

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Quadratic twists for elliptic curve 12390s4

-4	-3	5	-7
99120bo3	37170k3	61950g3	86730cd3

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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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