Cremona's table of elliptic curves

616 = 2³ · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 7- 11+	Signs for the Atkin-Lehner involutions
Class	616b	Isogeny class
Conductor	616	Conductor
∏ cp	20	Product of Tamagawa factors cp
Δ	384997945773056 = 210 · 710 · 113	Discriminant
Eigenvalues	2+  2  2 7- 11+  0  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-22792,936540]	[a1,a2,a3,a4,a6]
j	1278763167594532/375974556419	j-invariant
L	2.483500673188	L(r)(E,1)/r!
Ω	0.4967001346376	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	1232d2 4928r2 5544x2 15400m2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 616b2

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	4	4	-4	2	-2	-6	4	-4	2	2	-6	4	0	-12	16	-8	-12	10	-2

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Quadratic twists for elliptic curve 616b2

-4	8	-3	5	-7	-11	13
1232d2	4928r2	5544x2	15400m2	4312e2	6776f2	104104q2

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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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