Cremona's table of elliptic curves

31827 = 3 · 103²

Field	Data	Notes
Atkin-Lehner	3+ 103-	Signs for the Atkin-Lehner involutions
Class	31827a	Isogeny class
Conductor	31827	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	212160	Modular degree for the optimal curve
Δ	-29885934929824341 = -1 · 35 · 1037	Discriminant
Eigenvalues	-1 3+  1 -2  2 -5  0 -8	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-63875,-10408786]	[a1,a2,a3,a4,a6]
Generators	[314:628:1] [5902:145571:8]	Generators of the group modulo torsion
j	-24137569/25029	j-invariant
L	4.8123721556688	L(r)(E,1)/r!
Ω	0.14418380575279	Real period
R	8.3441620411904	Regulator
r	2	Rank of the group of rational points
S	1.0000000000003	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	95481d1 309a1	Quadratic twists by: -3 -103

Hecke Eigenvalues for elliptic curve 31827a1

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	-2	2	-5	0	-8	1	-2	-5	-2	8	11	2	-10	-11	-5	-11	-16	-12	6	1	6	-7

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Quadratic twists for elliptic curve 31827a1

-3	-103
95481d1	309a1

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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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