Cremona's table of elliptic curves

10416 = 2⁴ · 3 · 7 · 31

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 31+	Signs for the Atkin-Lehner involutions
Class	10416x	Isogeny class
Conductor	10416	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	3471777792 = 213 · 32 · 72 · 312	Discriminant
Eigenvalues	2- 3+  0 7-  6 -2  6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-1608,25200]	[a1,a2,a3,a4,a6]
Generators	[-6:186:1]	Generators of the group modulo torsion
j	112329015625/847602	j-invariant
L	4.2890974800636	L(r)(E,1)/r!
Ω	1.4151294543642	Real period
R	0.75772175238741	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	1302e2 41664dy2 31248bv2 72912cv2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416x2

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

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Quadratic twists for elliptic curve 10416x2

-4	8	-3	-7
1302e2	41664dy2	31248bv2	72912cv2

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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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