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	7854g	Isogeny class
Conductor	7854	Conductor
∏ cp	28	Product of Tamagawa factors cp
deg	43008	Modular degree for the optimal curve
Δ	-868557554027856 = -1 · 24 · 34 · 7 · 117 · 173	Discriminant
Eigenvalues	2+ 3+  1 7- 11- -1 17+  8	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-48722,4355268]	[a1,a2,a3,a4,a6]
Generators	[224:-2290:1]	Generators of the group modulo torsion
j	-12791249261627475241/868557554027856	j-invariant
L	3.0063960680893	L(r)(E,1)/r!
Ω	0.49139681001292	Real period
R	0.21850220831353	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	62832bj1 23562bf1 54978bf1 86394bu1	Quadratic twists by: -4 -3 -7 -11

Hecke Eigenvalues for elliptic curve 7854g1

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	-	-	-1	+	8	-1	-1	-10	4	0	-9	4	7	-9	-8	-8	-3	-6	-6	6	6	-2

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Quadratic twists for elliptic curve 7854g1

-4	-3	-7	-11
62832bj1	23562bf1	54978bf1	86394bu1

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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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