Cremona's table of elliptic curves

468 = 2² · 3² · 13

Field	Data	Notes
Atkin-Lehner	2- 3- 13-	Signs for the Atkin-Lehner involutions
Class	468d	Isogeny class
Conductor	468	Conductor
∏ cp	4	Product of Tamagawa factors cp
deg	96	Modular degree for the optimal curve
Δ	110539728 = 24 · 312 · 13	Discriminant
Eigenvalues	2- 3-  0  2  0 13-  6  2	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-120,-11]	[a1,a2,a3,a4,a6]
j	16384000/9477	j-invariant
L	1.5799514360134	L(r)(E,1)/r!
Ω	1.5799514360134	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	1872p1 7488k1 156b1 11700j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 468d1

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

---

Quadratic twists for elliptic curve 468d1

-4	8	-3	5	-7	-11	13
1872p1	7488k1	156b1	11700j1	22932k1	56628k1	6084f1

---

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