Cremona's table of elliptic curves

3472 = 2⁴ · 7 · 31

Field	Data	Notes
Atkin-Lehner	2+ 7- 31+	Signs for the Atkin-Lehner involutions
Class	3472b	Isogeny class
Conductor	3472	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	15274264951364608 = 210 · 75 · 316	Discriminant
Eigenvalues	2+  0  2 7- -2 -4  0  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-348619,79003818]	[a1,a2,a3,a4,a6]
j	4575904097608151172/14916274366567	j-invariant
L	1.9753298323946	L(r)(E,1)/r!
Ω	0.39506596647892	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	1736b2 13888r2 31248s2 86800b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3472b2

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

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Quadratic twists for elliptic curve 3472b2

-4	8	-3	5	-7	-31
1736b2	13888r2	31248s2	86800b2	24304g2	107632c2

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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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