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	1407c	Isogeny class
Conductor	1407	Conductor
∏ cp	48	Product of Tamagawa factors cp
Δ	280668001416201 = 312 · 76 · 672	Discriminant
Eigenvalues	-1 3-  2 7+ -4  2 -6 -8	Hecke eigenvalues for primes up to 20
Equation	[1,0,0,-18732,-570825]	[a1,a2,a3,a4,a6]
Generators	[-93:654:1]	Generators of the group modulo torsion
j	726904920233564353/280668001416201	j-invariant
L	2.2342596264526	L(r)(E,1)/r!
Ω	0.42166858851738	Real period
R	1.7662050935217	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	22512o2 90048c2 4221d2 35175h2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 1407c2

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	2	-6	-8	0	-2	8	-10	6	4	-4	-2	0	-14	-	0	2	-8	16	-14	-18

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Quadratic twists for elliptic curve 1407c2

-4	8	-3	5	-7	-67
22512o2	90048c2	4221d2	35175h2	9849j2	94269g2

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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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