Cremona's table of elliptic curves

121680 = 2⁴ · 3² · 5 · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 5+ 13+	Signs for the Atkin-Lehner involutions
Class	121680dg	Isogeny class
Conductor	121680	Conductor
∏ cp	2	Product of Tamagawa factors cp
Δ	30800250000 = 24 · 36 · 56 · 132	Discriminant
Eigenvalues	2- 3- 5+ -1 -3 13+  3  5	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-2613,-50713]	[a1,a2,a3,a4,a6]
Generators	[1886:81875:1]	Generators of the group modulo torsion
j	1000939264/15625	j-invariant
L	6.8757227803288	L(r)(E,1)/r!
Ω	0.66838324034669	Real period
R	5.1435482388064	Regulator
r	1	Rank of the group of rational points
S	0.99999998587246	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	30420f2 13520z2 121680er2	Quadratic twists by: -4 -3 13

Hecke Eigenvalues for elliptic curve 121680dg2

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	-3	+	3	5	9	9	8	7	3	1	0	-6	-9	-1	5	-9	-2	-8	0	3	-17

---

Quadratic twists for elliptic curve 121680dg2

-4	-3	13
30420f2	13520z2	121680er2

---

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