Cremona's table of elliptic curves

11305 = 5 · 7 · 17 · 19

Field	Data	Notes
Atkin-Lehner	5- 7- 17+ 19+	Signs for the Atkin-Lehner involutions
Class	11305h	Isogeny class
Conductor	11305	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	29952	Modular degree for the optimal curve
Δ	2172651425 = 52 · 72 · 173 · 192	Discriminant
Eigenvalues	1  2 5- 7-  0  2 17+ 19+	Hecke eigenvalues for primes up to 20
Equation	[1,1,0,-125377,17035224]	[a1,a2,a3,a4,a6]
Generators	[5556:-1598:27]	Generators of the group modulo torsion
j	217962984621942385561/2172651425	j-invariant
L	8.2410903408838	L(r)(E,1)/r!
Ω	1.0228880916204	Real period
R	4.0283440624616	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	101745v1 56525i1 79135o1	Quadratic twists by: -3 5 -7

Hecke Eigenvalues for elliptic curve 11305h1

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
1	2	-	-	0	2	+	+	-8	-4	-2	0	-8	4	8	-2	-4	-10	12	-14	6	-6	4	-14	-4

---

Quadratic twists for elliptic curve 11305h1

-3	5	-7
101745v1	56525i1	79135o1

---

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