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	12350p	Isogeny class
Conductor	12350	Conductor
∏ cp	1144	Product of Tamagawa factors cp
deg	15759744	Modular degree for the optimal curve
Δ	-2.7894618101107E+30	Discriminant
Eigenvalues	2-  1 5+  1  0 13- -4 19+	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,2042757537,72071331491417]	[a1,a2,a3,a4,a6]
Generators	[-11468:6871359:1]	Generators of the group modulo torsion
j	60332893035582377081137649111/178525555847085424640000000	j-invariant
L	8.2093223898296	L(r)(E,1)/r!
Ω	0.017953812318516	Real period
R	0.39969121781396	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	98800cd1 111150bl1 2470a1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 12350p1

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	+	1	0	-	-4	+	-6	6	-1	-2	-9	-6	11	2	4	7	4	-11	-2	-10	-9	1	-4

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Quadratic twists for elliptic curve 12350p1

-4	-3	5
98800cd1	111150bl1	2470a1

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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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