Cremona's table of elliptic curves

30300 = 2² · 3 · 5² · 101

Field	Data	Notes
Atkin-Lehner	2- 3+ 5+ 101-	Signs for the Atkin-Lehner involutions
Class	30300c	Isogeny class
Conductor	30300	Conductor
∏ cp	24	Product of Tamagawa factors cp
deg	46080	Modular degree for the optimal curve
Δ	1032851250000 = 24 · 34 · 57 · 1012	Discriminant
Eigenvalues	2- 3+ 5+ -4  4  2 -2  8	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-2533,5062]	[a1,a2,a3,a4,a6]
Generators	[-23:225:1]	Generators of the group modulo torsion
j	7192182784/4131405	j-invariant
L	4.2575294749619	L(r)(E,1)/r!
Ω	0.74796004511189	Real period
R	0.94869806276997	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	121200ds1 90900i1 6060d1	Quadratic twists by: -4 -3 5

Hecke Eigenvalues for elliptic curve 30300c1

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
-	+	+	-4	4	2	-2	8	-2	-6	0	2	6	-6	6	-4	-4	2	4	-12	-16	-16	8	6	-2

---

Quadratic twists for elliptic curve 30300c1

-4	-3	5
121200ds1	90900i1	6060d1

---

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