Cremona's table of elliptic curves

31248 = 2⁴ · 3² · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 7+ 31-	Signs for the Atkin-Lehner involutions
Class	31248ba	Isogeny class
Conductor	31248	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	1075200	Modular degree for the optimal curve
Δ	-6.631619771388E+20	Discriminant
Eigenvalues	2- 3+ -1 7+ -5 -1  5 -1	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-6155043,6006699554]	[a1,a2,a3,a4,a6]
Generators	[2737:98304:1]	Generators of the group modulo torsion
j	-233181060948366864507/5996473317588992	j-invariant
L	4.1375301573321	L(r)(E,1)/r!
Ω	0.16126296636324	Real period
R	1.6035649142828	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	3906a1 124992dn1 31248z1	Quadratic twists by: -4 8 -3

Hecke Eigenvalues for elliptic curve 31248ba1

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	+	-5	-1	5	-1	-6	6	-	-2	0	4	-1	0	-6	7	5	15	-8	-1	5	6	17

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Quadratic twists for elliptic curve 31248ba1

-4	8	-3
3906a1	124992dn1	31248z1

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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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