Cremona's table of elliptic curves

6307 = 7 · 17 · 53

Field	Data	Notes
Atkin-Lehner	7+ 17+ 53+	Signs for the Atkin-Lehner involutions
Class	6307a	Isogeny class
Conductor	6307	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	2112	Modular degree for the optimal curve
Δ	2339897 = 72 · 17 · 532	Discriminant
Eigenvalues	-1  2 -4 7+  4 -6 17+  4	Hecke eigenvalues for primes up to 20
Equation	[1,1,1,-35,16]	[a1,a2,a3,a4,a6]
Generators	[-4:12:1]	Generators of the group modulo torsion
j	4750104241/2339897	j-invariant
L	2.5312014610773	L(r)(E,1)/r!
Ω	2.2959641029699	Real period
R	1.102456897215	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	100912t1 56763m1 44149k1 107219h1	Quadratic twists by: -4 -3 -7 17

Hecke Eigenvalues for elliptic curve 6307a1

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

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Quadratic twists for elliptic curve 6307a1

-4	-3	-7	17
100912t1	56763m1	44149k1	107219h1

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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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