Cremona's table of elliptic curves

414 = 2 · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 23-	Signs for the Atkin-Lehner involutions
Class	414b	Isogeny class
Conductor	414	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	64	Modular degree for the optimal curve
Δ	-603612 = -1 · 22 · 38 · 23	Discriminant
Eigenvalues	2- 3-  2 -2  6 -2  0  0	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-14,-39]	[a1,a2,a3,a4,a6]
j	-389017/828	j-invariant
L	2.326716093051	L(r)(E,1)/r!
Ω	1.1633580465255	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	3312o1 13248v1 138a1 10350j1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 414b1

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

---

Quadratic twists for elliptic curve 414b1

-4	8	-3	5	-7	-11	13	17	-23
3312o1	13248v1	138a1	10350j1	20286cs1	50094bc1	69966r1	119646cd1	9522k1

---

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