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	32	Product of Tamagawa factors cp
Δ	445421025 = 34 · 52 · 72 · 672	Discriminant
Eigenvalues	1 3- 5+ 7+  0  2 -2  4	Hecke eigenvalues for primes up to 20
Equation	[1,0,1,-199,341]	[a1,a2,a3,a4,a6]
Generators	[1:11:1]	Generators of the group modulo torsion
j	865250742889/445421025	j-invariant
L	5.3717895036029	L(r)(E,1)/r!
Ω	1.4722797882721	Real period
R	1.8243100076472	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	4	Number of elements in the torsion subgroup
Twists	112560bj2 21105j2 35175i2 49245r2	Quadratic twists by: -4 -3 5 -7

Hecke Eigenvalues for elliptic curve 7035g2

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 7035g2

-4	-3	5	-7
112560bj2	21105j2	35175i2	49245r2

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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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