Cremona's table of elliptic curves

97344 = 2⁶ · 3² · 13²

Field	Data	Notes
Atkin-Lehner	2- 3- 13+	Signs for the Atkin-Lehner involutions
Class	97344er	Isogeny class
Conductor	97344	Conductor
∏ cp	32	Product of Tamagawa factors cp
Δ	-29229106574573568 = -1 · 214 · 37 · 138	Discriminant
Eigenvalues	2- 3-  0 -4 -2 13+  6  4	Hecke eigenvalues for primes up to 20
Equation	[0,0,0,70980,-3831568]	[a1,a2,a3,a4,a6]
Generators	[1924:85176:1]	Generators of the group modulo torsion
j	686000/507	j-invariant
L	5.4676083405639	L(r)(E,1)/r!
Ω	0.20889805286503	Real period
R	3.2716965610998	Regulator
r	1	Rank of the group of rational points
S	1.000000002036	(Analytic) order of Ш
t	2	Number of elements in the torsion subgroup
Twists	97344z2 24336d2 32448bz2 7488by2	Quadratic twists by: -4 8 -3 13

Hecke Eigenvalues for elliptic curve 97344er2

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

---

Quadratic twists for elliptic curve 97344er2

-4	8	-3	13
97344z2	24336d2	32448bz2	7488by2

---

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