Cremona's table of elliptic curves

6930 = 2 · 3² · 5 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2+ 3+ 5+ 7- 11-	Signs for the Atkin-Lehner involutions
Class	6930b	Isogeny class
Conductor	6930	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	1536	Modular degree for the optimal curve
Δ	-13305600 = -1 · 28 · 33 · 52 · 7 · 11	Discriminant
Eigenvalues	2+ 3+ 5+ 7- 11- -2 -2 -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,0,-75,325]	[a1,a2,a3,a4,a6]
Generators	[5:5:1]	Generators of the group modulo torsion
j	-1740992427/492800	j-invariant
L	2.8732766893483	L(r)(E,1)/r!
Ω	2.1235405246808	Real period
R	0.67652975207058	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	55440bv1 6930u1 34650cn1 48510k1	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 6930b1

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

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Quadratic twists for elliptic curve 6930b1

-4	-3	5	-7	-11
55440bv1	6930u1	34650cn1	48510k1	76230cs1

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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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