Cremona's table of elliptic curves

426 = 2 · 3 · 71

Field	Data	Notes
Atkin-Lehner	2+ 3+ 71+	Signs for the Atkin-Lehner involutions
Class	426b	Isogeny class
Conductor	426	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	4355424 = 25 · 33 · 712	Discriminant
Eigenvalues	2+ 3+ -2  2 -2  0  0 -4	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-4606,118420]	[a1,a2,a3,a4,a6]
Generators	[21:167:1]	Generators of the group modulo torsion
j	10810426566289897/4355424	j-invariant
L	1.2152039603397	L(r)(E,1)/r!
Ω	1.9951714954238	Real period
R	1.2181448693778	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	3408h2 13632h2 1278k2 10650be2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 426b2

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
+	+	-2	2	-2	0	0	-4	-4	-6	-2	-6	0	-4	0	6	-10	0	4	+	10	-8	-8	6	18

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Quadratic twists for elliptic curve 426b2

-4	8	-3	5	-7	-11	13	17	-71
3408h2	13632h2	1278k2	10650be2	20874n2	51546e2	71994bj2	123114h2	30246a2

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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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