Cremona's table of elliptic curves

1892 = 2² · 11 · 43

Field	Data	Notes
Atkin-Lehner	2- 11+ 43-	Signs for the Atkin-Lehner involutions
Class	1892b	Isogeny class
Conductor	1892	Conductor
∏ cp	1	Product of Tamagawa factors cp
deg	72	Modular degree for the optimal curve
Δ	7568 = 24 · 11 · 43	Discriminant
Eigenvalues	2-  0  0  3 11+ -2  2 -7	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-5,1]	[a1,a2,a3,a4,a6]
Generators	[0:1:1]	Generators of the group modulo torsion
j	864000/473	j-invariant
L	3.0404896199744	L(r)(E,1)/r!
Ω	3.6301173912983	Real period
R	0.83757335982101	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	7568k1 30272k1 17028q1 47300a1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1892b1

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
-	0	0	3	+	-2	2	-7	-5	-3	-3	8	0	-	7	-5	-3	-11	3	-12	2	-14	8	16	1

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Quadratic twists for elliptic curve 1892b1

-4	8	-3	5	-7	-11	-43
7568k1	30272k1	17028q1	47300a1	92708d1	20812g1	81356a1

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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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