Cremona's table of elliptic curves

12726 = 2 · 3² · 7 · 101

Field	Data	Notes
Atkin-Lehner	2- 3+ 7- 101+	Signs for the Atkin-Lehner involutions
Class	12726h	Isogeny class
Conductor	12726	Conductor
∏ cp	260	Product of Tamagawa factors cp
deg	287040	Modular degree for the optimal curve
Δ	-4600266694105227264 = -1 · 213 · 39 · 710 · 101	Discriminant
Eigenvalues	2- 3+  3 7- -4 -4  4 -6	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,254959,90453889]	[a1,a2,a3,a4,a6]
Generators	[-209:5396:1]	Generators of the group modulo torsion
j	93120448241218581/233717761220608	j-invariant
L	8.2962160295631	L(r)(E,1)/r!
Ω	0.17089567191082	Real period
R	0.18671346578794	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	101808m1 12726c1 89082bf1	Quadratic twists by: -4 -3 -7

Hecke Eigenvalues for elliptic curve 12726h1

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
-	+	3	-	-4	-4	4	-6	0	-8	-5	0	-5	4	-12	6	-8	3	11	-8	-6	-9	6	11	1

---

Quadratic twists for elliptic curve 12726h1

-4	-3	-7
101808m1	12726c1	89082bf1

---

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