Cremona's table of elliptic curves

12350 = 2 · 5² · 13 · 19

Field	Data	Notes
Atkin-Lehner	2+ 5- 13- 19+	Signs for the Atkin-Lehner involutions
Class	12350k	Isogeny class
Conductor	12350	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	-88096996000 = -1 · 25 · 53 · 132 · 194	Discriminant
Eigenvalues	2+  2 5-  0  4 13-  4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,365,-13875]	[a1,a2,a3,a4,a6]
Generators	[3540:25335:64]	Generators of the group modulo torsion
j	42838260499/704775968	j-invariant
L	5.2130870536334	L(r)(E,1)/r!
Ω	0.52469485678484	Real period
R	4.967732183976	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	98800df2 111150ff2 12350w2	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12350k2

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

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Quadratic twists for elliptic curve 12350k2

-4	-3	5
98800df2	111150ff2	12350w2

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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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