Cremona's table of elliptic curves

11312 = 2⁴ · 7 · 101

Field	Data	Notes
Atkin-Lehner	2+ 7- 101-	Signs for the Atkin-Lehner involutions
Class	11312g	Isogeny class
Conductor	11312	Conductor
∏ cp	10	Product of Tamagawa factors cp
deg	18240	Modular degree for the optimal curve
Δ	-434561792 = -1 · 28 · 75 · 101	Discriminant
Eigenvalues	2+ -1  0 7- -6  2  0 -2	Hecke eigenvalues for primes up to 20
Equation	[0,-1,0,-79588,8668688]	[a1,a2,a3,a4,a6]
Generators	[172:196:1]	Generators of the group modulo torsion
j	-217787012453554000/1697507	j-invariant
L	3.3659714812668	L(r)(E,1)/r!
Ω	1.1570909866092	Real period
R	0.29089946427899	Regulator
r	1	Rank of the group of rational points
S	1	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	5656a1 45248bb1 101808k1 79184c1	Quadratic twists by: -4 8 -3 -7

Hecke Eigenvalues for elliptic curve 11312g1

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	0	-	-6	2	0	-2	-1	8	2	3	6	-1	10	0	1	-1	2	-9	13	-15	11	-7	12

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Quadratic twists for elliptic curve 11312g1

-4	8	-3	-7
5656a1	45248bb1	101808k1	79184c1

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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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