Cremona's table of elliptic curves

1872 = 2⁴ · 3² · 13

Field	Data	Notes
Atkin-Lehner	2+ 3+ 13+	Signs for the Atkin-Lehner involutions
Class	1872b	Isogeny class
Conductor	1872	Conductor
∏ cp	8	Product of Tamagawa factors cp
Δ	4672512 = 210 · 33 · 132	Discriminant
Eigenvalues	2+ 3+ -2 -2  4 13+  0  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-51,-94]	[a1,a2,a3,a4,a6]
Generators	[-5:6:1]	Generators of the group modulo torsion
j	530604/169	j-invariant
L	2.6380281509813	L(r)(E,1)/r!
Ω	1.8314537416018	Real period
R	0.72020059558647	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	936a2 7488bh2 1872a2 46800e2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872b2

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

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Quadratic twists for elliptic curve 1872b2

-4	8	-3	5	-7	13
936a2	7488bh2	1872a2	46800e2	91728h2	24336a2

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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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