Cremona's table of elliptic curves

3312 = 2⁴ · 3² · 23

Field	Data	Notes
Atkin-Lehner	2- 3- 23+	Signs for the Atkin-Lehner involutions
Class	3312p	Isogeny class
Conductor	3312	Conductor
∏ cp	16	Product of Tamagawa factors cp
Δ	901187887104 = 213 · 314 · 23	Discriminant
Eigenvalues	2- 3- -2  0  0 -2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,-35571,2581810]	[a1,a2,a3,a4,a6]
Generators	[113:72:1]	Generators of the group modulo torsion
j	1666957239793/301806	j-invariant
L	3.0706456155783	L(r)(E,1)/r!
Ω	0.85894175962466	Real period
R	0.89372928407861	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	414c3 13248be4 1104h3 82800dq4	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3312p4

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	0	0	-2	-2	8	+	2	8	2	-10	-8	8	-2	-4	2	-8	0	-6	-8	-16	-18	10

---

Quadratic twists for elliptic curve 3312p4

-4	8	-3	5	-23
414c3	13248be4	1104h3	82800dq4	76176ca4

---

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