Cremona's table of elliptic curves

1848 = 2³ · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	1848b	Isogeny class
Conductor	1848	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	450793728 = 28 · 33 · 72 · 113	Discriminant
Eigenvalues	2+ 3+  2 7- 11- -6 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-586972,-172895372]	[a1,a2,a3,a4,a6]
Generators	[5958:455840:1]	Generators of the group modulo torsion
j	87364831012240243408/1760913	j-invariant
L	2.8456276537344	L(r)(E,1)/r!
Ω	0.17248254309111	Real period
R	5.4993539302337	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	3696i1 14784bf1 5544t1 46200cu1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1848b1

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

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Quadratic twists for elliptic curve 1848b1

-4	8	-3	5	-7	-11
3696i1	14784bf1	5544t1	46200cu1	12936k1	20328p1

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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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