Cremona's table of elliptic curves

248 = 2³ · 31

Field	Data	Notes
Atkin-Lehner	2- 31+	Signs for the Atkin-Lehner involutions
Class	248b	Isogeny class
Conductor	248	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	1968128 = 211 · 312	Discriminant
Eigenvalues	2- -2  2  0  2  4  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-32,-32]	[a1,a2,a3,a4,a6]
j	1825346/961	j-invariant
L	1.061759246798	L(r)(E,1)/r!
Ω	2.1235184935959	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	496c2 1984d2 2232c2 6200b2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 248b2

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

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Quadratic twists for elliptic curve 248b2

-4	8	-3	5	-7	-11	13	17	-19	-31
496c2	1984d2	2232c2	6200b2	12152h2	30008a2	41912d2	71672h2	89528f2	7688l2

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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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