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	10416n	Isogeny class
Conductor	10416	Conductor
∏ cp	192	Product of Tamagawa factors cp
Δ	18755411576832 = 211 · 34 · 76 · 312	Discriminant
Eigenvalues	2+ 3- -4 7- -6 -6 -6 -6	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7000,-88396]	[a1,a2,a3,a4,a6]
Generators	[-70:252:1] [-46:372:1]	Generators of the group modulo torsion
j	18524646126002/9157915809	j-invariant
L	5.7872983291488	L(r)(E,1)/r!
Ω	0.54907770578496	Real period
R	0.21958406600787	Regulator
r	2	Rank of the group of rational points
S	1.0000000000005	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	5208a2 41664dc2 31248x2 72912j2	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416n2

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

---

Quadratic twists for elliptic curve 10416n2

-4	8	-3	-7
5208a2	41664dc2	31248x2	72912j2

---

Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
Back to Tables and computations