Cremona's table of elliptic curves

7035 = 3 · 5 · 7 · 67

Field	Data	Notes
Atkin-Lehner	3- 5+ 7+ 67-	Signs for the Atkin-Lehner involutions
Class	7035g	Isogeny class
Conductor	7035	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	1923193125 = 38 · 54 · 7 · 67	Discriminant
Eigenvalues	1 3- 5+ 7+  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-2544,49117]	[a1,a2,a3,a4,a6]
Generators	[11:144:1]	Generators of the group modulo torsion
j	1819824927790969/1923193125	j-invariant
L	5.3717895036029	L(r)(E,1)/r!
Ω	1.4722797882721	Real period
R	0.91215500382359	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	112560bj4 21105j4 35175i4 49245r4	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7035g4

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
1	-	+	+	0	2	-2	4	0	-2	8	-2	-2	-12	-12	-6	4	-6	-	0	6	12	-8	10	14

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Quadratic twists for elliptic curve 7035g4

-4	-3	5	-7
112560bj4	21105j4	35175i4	49245r4

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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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