Cremona's table of elliptic curves

30135 = 3 · 5 · 7² · 41

Field	Data	Notes
Atkin-Lehner	3+ 5- 7- 41+	Signs for the Atkin-Lehner involutions
Class	30135o	Isogeny class
Conductor	30135	Conductor
∏ cp	8	Product of Tamagawa factors cp
deg	325248	Modular degree for the optimal curve
Δ	-15330111943426875 = -1 · 311 · 54 · 72 · 414	Discriminant
Eigenvalues	-2 3+ 5- 7- -2 -1 -4 -5	Hecke eigenvalues for primes up to 20
Equation	[0,-1,1,44000,4767258]	[a1,a2,a3,a4,a6]
Generators	[174:4202:1]	Generators of the group modulo torsion
j	192254180071632896/312859427416875	j-invariant
L	2.1276017495029	L(r)(E,1)/r!
Ω	0.2685170234239	Real period
R	0.99044081189601	Regulator
r	1	Rank of the group of rational points
S	0.99999999999997	(Analytic) order of Ш
t	1	Number of elements in the torsion subgroup
Twists	90405ba1 30135x1	Quadratic twists by: -3 -7

Hecke Eigenvalues for elliptic curve 30135o1

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	+	-	-	-2	-1	-4	-5	8	0	7	7	+	-7	-6	-12	0	6	3	-10	7	11	10	8	-18

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Quadratic twists for elliptic curve 30135o1

-3	-7
90405ba1	30135x1

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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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