Cremona's table of elliptic curves

840 = 2³ · 3 · 5 · 7

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7+	Signs for the Atkin-Lehner involutions
Class	840a	Isogeny class
Conductor	840	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-82978560000 = -1 · 211 · 33 · 54 · 74	Discriminant
Eigenvalues	2+ 3+ 5+ 7+  4 -2 -6  0	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,744,-11700]	[a1,a2,a3,a4,a6]
Generators	[209:3038:1]	Generators of the group modulo torsion
j	22208984782/40516875	j-invariant
L	1.9611172164749	L(r)(E,1)/r!
Ω	0.56602435748099	Real period
R	3.4647223048892	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	1680g4 6720bb4 2520r4 4200ba4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 840a4

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
+	+	+	+	4	-2	-6	0	0	-6	0	-6	-10	0	-12	-6	-4	2	8	-4	10	0	12	-10	-14

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Quadratic twists for elliptic curve 840a4

-4	8	-3	5	-7	-11
1680g4	6720bb4	2520r4	4200ba4	5880p4	101640bv3

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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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