Cremona's table of elliptic curves

10400 = 2⁵ · 5² · 13

Field	Data	Notes
Atkin-Lehner	2- 5- 13+	Signs for the Atkin-Lehner involutions
Class	10400bd	Isogeny class
Conductor	10400	Conductor
∏ cp	4	Product of Tamagawa factors cp
Δ	-169000000000 = -1 · 29 · 59 · 132	Discriminant
Eigenvalues	2-  2 5-  0  0 13+  4 -8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,792,-18088]	[a1,a2,a3,a4,a6]
Generators	[2315535:60656428:3375]	Generators of the group modulo torsion
j	54872/169	j-invariant
L	6.2386891097959	L(r)(E,1)/r!
Ω	0.52119797105149	Real period
R	11.969902908888	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	10400r2 20800cb2 93600bz2 10400t2	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400bd2

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	-	0	0	+	4	-8	-4	6	2	2	2	2	-8	-10	-12	10	4	-10	-10	8	12	6	-14

---

Quadratic twists for elliptic curve 10400bd2

-4	8	-3	5
10400r2	20800cb2	93600bz2	10400t2

---

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