Cremona's table of elliptic curves

1407 = 3 · 7 · 67

Field	Data	Notes
Atkin-Lehner	3- 7+ 67+	Signs for the Atkin-Lehner involutions
Class	1407b	Isogeny class
Conductor	1407	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	-6499187667 = -1 · 32 · 74 · 673	Discriminant
Eigenvalues	2 3-  4 7+ -2  4 -3  7	Hecke eigenvalues for primes up to 20
Equation	[0,1,1,-3946,94183]	[a1,a2,a3,a4,a6]
j	-6796808121217024/6499187667	j-invariant
L	5.3149700126014	L(r)(E,1)/r!
Ω	1.3287425031504	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	22512p1 90048f1 4221c1 35175o1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1407b1

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	-	4	+	-2	4	-3	7	-9	1	0	3	8	-10	-3	-6	-9	-2	+	0	-3	-4	12	-11	12

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Quadratic twists for elliptic curve 1407b1

-4	8	-3	5	-7	-67
22512p1	90048f1	4221c1	35175o1	9849g1	94269i1

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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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