Cremona's table of elliptic curves

7854 = 2 · 3 · 7 · 11 · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11+ 17-	Signs for the Atkin-Lehner involutions
Class	7854q	Isogeny class
Conductor	7854	Conductor
∏ cp	48	Product of Tamagawa factors cp
deg	3072	Modular degree for the optimal curve
Δ	-434294784 = -1 · 212 · 34 · 7 · 11 · 17	Discriminant
Eigenvalues	2- 3- -1 7- 11+ -3 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-251,1809]	[a1,a2,a3,a4,a6]
Generators	[-2:49:1]	Generators of the group modulo torsion
j	-1749254553649/434294784	j-invariant
L	7.0651659473966	L(r)(E,1)/r!
Ω	1.5944833572513	Real period
R	0.09231263315985	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	62832ba1 23562p1 54978bi1 86394u1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854q1

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
-	-	-1	-	+	-3	-	-4	-3	3	-2	-4	-8	1	-4	-9	3	12	-4	-9	-2	-10	-2	14	-6

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Quadratic twists for elliptic curve 7854q1

-4	-3	-7	-11
62832ba1	23562p1	54978bi1	86394u1

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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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