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	7854n	Isogeny class
Conductor	7854	Conductor
∏ cp	160	Product of Tamagawa factors cp
deg	7680	Modular degree for the optimal curve
Δ	9690202368 = 28 · 35 · 72 · 11 · 172	Discriminant
Eigenvalues	2- 3-  0 7+ 11+ -2 17+  6	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-2638,51716]	[a1,a2,a3,a4,a6]
Generators	[62:-388:1]	Generators of the group modulo torsion
j	2030291400390625/9690202368	j-invariant
L	7.1553678703635	L(r)(E,1)/r!
Ω	1.2990502899292	Real period
R	0.13770382728511	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	62832bh1 23562k1 54978bn1 86394bi1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854n1

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	+	+	-2	+	6	-8	-6	-8	6	-6	-2	2	-2	6	-8	4	-12	-4	-4	0	-2	6

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Quadratic twists for elliptic curve 7854n1

-4	-3	-7	-11
62832bh1	23562k1	54978bn1	86394bi1

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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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