Cremona's table of elliptic curves

40296 = 2³ · 3 · 23 · 73

Field	Data	Notes
Atkin-Lehner	2+ 3- 23- 73+	Signs for the Atkin-Lehner involutions
Class	40296f	Isogeny class
Conductor	40296	Conductor
∏ cp	88	Product of Tamagawa factors cp
Δ	541029341262403584 = 211 · 311 · 234 · 732	Discriminant
Eigenvalues	2+ 3- -2 -2 -2  4  4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-7571144,-8020895184]	[a1,a2,a3,a4,a6]
Generators	[6871:514188:1]	Generators of the group modulo torsion
j	23435721924943450307474/264174483038283	j-invariant
L	5.8295146164966	L(r)(E,1)/r!
Ω	0.091014265170649	Real period
R	2.9113890730959	Regulator
r	1	Rank of the group of rational points
S	0.99999999999926	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	80592a2 120888f2	Quadratic twists by: -4 -3

Hecke Eigenvalues for elliptic curve 40296f2

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

---

Quadratic twists for elliptic curve 40296f2

-4	-3
80592a2	120888f2

---

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