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	1872i	Isogeny class
Conductor	1872	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	256	Modular degree for the optimal curve
Δ	12282192 = 24 · 310 · 13	Discriminant
Eigenvalues	2+ 3- -2  0  0 13- -2  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-66,119]	[a1,a2,a3,a4,a6]
Generators	[-5:18:1]	Generators of the group modulo torsion
j	2725888/1053	j-invariant
L	2.7085124774504	L(r)(E,1)/r!
Ω	2.0526958914417	Real period
R	1.3194903778699	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	936e1 7488br1 624c1 46800k1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1872i1

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	0	-	-2	4	0	-6	0	-2	-6	12	-4	-6	-8	-2	-4	-12	-14	0	8	18	-6

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Quadratic twists for elliptic curve 1872i1

-4	8	-3	5	-7	13
936e1	7488br1	624c1	46800k1	91728w1	24336f1

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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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