Cremona's table of elliptic curves

322 = 2 · 7 · 23

Field	Data	Notes
Atkin-Lehner	2+ 7- 23+	Signs for the Atkin-Lehner involutions
Class	322b	Isogeny class
Conductor	322	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	112	Modular degree for the optimal curve
Δ	-60669952 = -1 · 214 · 7 · 232	Discriminant
Eigenvalues	2+  2  0 7-  4  0  6 -6	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,35,381]	[a1,a2,a3,a4,a6]
j	4533086375/60669952	j-invariant
L	1.4602213360674	L(r)(E,1)/r!
Ω	1.4602213360674	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	2576n1 10304j1 2898t1 8050p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 322b1

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

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Quadratic twists for elliptic curve 322b1

-4	8	-3	5	-7	-11	13	17	-19	-23
2576n1	10304j1	2898t1	8050p1	2254a1	38962w1	54418f1	93058b1	116242x1	7406c1

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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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