Cremona's table of elliptic curves

12100 = 2² · 5² · 11²

Field	Data	Notes
Atkin-Lehner	2- 5+ 11-	Signs for the Atkin-Lehner involutions
Class	12100h	Isogeny class
Conductor	12100	Conductor
∏ cp	16	Product of Tamagawa factors cp
deg	34560	Modular degree for the optimal curve
Δ	267948601250000 = 24 · 57 · 118	Discriminant
Eigenvalues	2- -2 5+  0 11-  0 -4  4	Hecke eigenvalues for primes up to 20
Equation	[0,1,0,-16133,-48512]	[a1,a2,a3,a4,a6]
Generators	[348:6050:1]	Generators of the group modulo torsion
j	1048576/605	j-invariant
L	2.9470138833476	L(r)(E,1)/r!
Ω	0.46204528555643	Real period
R	1.5945481836259	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	48400ce1 108900bj1 2420f1 1100c1	Quadratic twists by: -4 -3 5 -11

Hecke Eigenvalues for elliptic curve 12100h1

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

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Quadratic twists for elliptic curve 12100h1

-4	-3	5	-11
48400ce1	108900bj1	2420f1	1100c1

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Data from Elliptic Curve Data by J. E. Cremona.
Design inspired by The Modular Forms Explorer by William Stein.

Part of Computational Number Theory
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