Cremona's table of elliptic curves

25350 = 2 · 3 · 5² · 13²

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 13+	Signs for the Atkin-Lehner involutions
Class	25350g	Isogeny class
Conductor	25350	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	764747550937500000 = 25 · 3 · 510 · 138	Discriminant
Eigenvalues	2+ 3+ 5+  4  0 13+  2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-365583000,2690311164000]	[a1,a2,a3,a4,a6]
Generators	[92343889015:-46214193570:8365427]	Generators of the group modulo torsion
j	71647584155243142409/10140000	j-invariant
L	3.8393366094849	L(r)(E,1)/r!
Ω	0.16257873325326	Real period
R	11.807622475149	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	76050ew4 5070w4 1950q4	Quadratic twists by: -3 5 13

Hecke Eigenvalues for elliptic curve 25350g4

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	0	+	2	-4	-8	2	8	2	6	-12	0	-10	0	-10	-4	16	-6	-8	-4	14	-6

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Quadratic twists for elliptic curve 25350g4

-3	5	13
76050ew4	5070w4	1950q4

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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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