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	10400h	Isogeny class
Conductor	10400	Conductor
∏ cp	14	Product of Tamagawa factors cp
deg	120960	Modular degree for the optimal curve
Δ	2509940680000000000 = 212 · 510 · 137	Discriminant
Eigenvalues	2+  1 5+ -2  2 13-  2  2	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-978333,-364902037]	[a1,a2,a3,a4,a6]
j	2588953638400/62748517	j-invariant
L	2.1283711185232	L(r)(E,1)/r!
Ω	0.15202650846594	Real period
R	1	Regulator
r	0	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	10400w1 20800j1 93600eh1 10400ba1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 10400h1

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	2	-	2	2	-1	-3	4	10	-2	-3	6	-11	-14	11	10	0	-2	-3	6	12	-10

---

Quadratic twists for elliptic curve 10400h1

-4	8	-3	5
10400w1	20800j1	93600eh1	10400ba1

---

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