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	7854t	Isogeny class
Conductor	7854	Conductor
∏ cp	300	Product of Tamagawa factors cp
deg	19200	Modular degree for the optimal curve
Δ	-8654638519296 = -1 · 210 · 32 · 73 · 115 · 17	Discriminant
Eigenvalues	2- 3- -3 7- 11-  1 17+ -2	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,3958,104484]	[a1,a2,a3,a4,a6]
Generators	[178:2452:1]	Generators of the group modulo torsion
j	6857159064725087/8654638519296	j-invariant
L	6.5022342362009	L(r)(E,1)/r!
Ω	0.49242632396562	Real period
R	0.044014938003564	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	62832v1 23562o1 54978bu1 86394bc1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854t1

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
-	-	-3	-	-	1	+	-2	-9	-5	4	0	-2	-1	-8	-9	9	0	12	-7	-2	-4	-4	2	6

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Quadratic twists for elliptic curve 7854t1

-4	-3	-7	-11
62832v1	23562o1	54978bu1	86394bc1

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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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