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	10416o	Isogeny class
Conductor	10416	Conductor
∏ cp	2	Product of Tamagawa factors cp
deg	3456	Modular degree for the optimal curve
Δ	1575555408 = 24 · 33 · 76 · 31	Discriminant
Eigenvalues	2- 3+  0 7+  0 -4 -6  4	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-393,2448]	[a1,a2,a3,a4,a6]
j	420616192000/98472213	j-invariant
L	0.7071685944667	L(r)(E,1)/r!
Ω	1.4143371889334	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	2604f1 41664de1 31248bh1 72912ct1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 10416o1

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

---

Quadratic twists for elliptic curve 10416o1

-4	8	-3	-7
2604f1	41664de1	31248bh1	72912ct1

---

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