Cremona's table of elliptic curves

306 = 2 · 3² · 17

Field	Data	Notes
Atkin-Lehner	2- 3- 17-	Signs for the Atkin-Lehner involutions
Class	306a	Isogeny class
Conductor	306	Conductor
∏ cp	12	Product of Tamagawa factors cp
deg	192	Modular degree for the optimal curve
Δ	578207808 = 26 · 312 · 17	Discriminant
Eigenvalues	2- 3-  0  2  0  2 17- -4	Hecke eigenvalues for primes up to 20
Equation	[1,-1,1,-2300,-41857]	[a1,a2,a3,a4,a6]
j	1845026709625/793152	j-invariant
L	2.0683060777422	L(r)(E,1)/r!
Ω	0.6894353592474	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	2448p1 9792p1 102c1 7650p1	Quadratic twists by: -4 8 -3 5

Hecke Eigenvalues for elliptic curve 306a1

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	2	0	2	-	-4	6	0	-10	8	-6	-4	-12	-6	12	8	-4	-6	2	-10	-12	18	14

---

Quadratic twists for elliptic curve 306a1

-4	8	-3	5	-7	-11	13	17	-19
2448p1	9792p1	102c1	7650p1	14994ce1	37026g1	51714f1	5202h1	110466q1

---

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