Cremona's table of elliptic curves

434 = 2 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 7- 31+	Signs for the Atkin-Lehner involutions
Class	434d	Isogeny class
Conductor	434	Conductor
∏ cp	20	Product of Tamagawa factors cp
deg	80	Modular degree for the optimal curve
Δ	-1555456 = -1 · 210 · 72 · 31	Discriminant
Eigenvalues	2- -2 -2 7- -2 -4 -2 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,21,49]	[a1,a2,a3,a4,a6]
Generators	[0:7:1]	Generators of the group modulo torsion
j	1021147343/1555456	j-invariant
L	1.87890542232	L(r)(E,1)/r!
Ω	1.8196638477539	Real period
R	0.20651126576365	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	3472e1 13888i1 3906k1 10850b1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 434d1

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

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Quadratic twists for elliptic curve 434d1

-4	8	-3	5	-7	-11	13	17	-31
3472e1	13888i1	3906k1	10850b1	3038k1	52514c1	73346i1	125426o1	13454h1

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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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