Cremona's table of elliptic curves

3696 = 2⁴ · 3 · 7 · 11

Field	Data	Notes
Atkin-Lehner	2- 3- 7- 11+	Signs for the Atkin-Lehner involutions
Class	3696z	Isogeny class
Conductor	3696	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	11520	Modular degree for the optimal curve
Δ	62504659058688 = 232 · 33 · 72 · 11	Discriminant
Eigenvalues	2- 3-  2 7- 11+  2  6  8	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-10312,129908]	[a1,a2,a3,a4,a6]
j	29609739866953/15259926528	j-invariant
L	3.2894895535275	L(r)(E,1)/r!
Ω	0.54824825892125	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	462b1 14784cb1 11088bz1 92400dl1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 3696z1

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	8	-4	2	-8	6	6	-8	-4	10	-4	-14	4	4	-14	8	-4	-14	18

---

Quadratic twists for elliptic curve 3696z1

-4	8	-3	5	-7	-11
462b1	14784cb1	11088bz1	92400dl1	25872bo1	40656cl1

---

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