Cremona's table of elliptic curves

31713 = 3 · 11 · 31²

Class	r	Atkin-Lehner	Eigenvalues
31713a (1 curve)	1	3+ 11+ 31+	0 3+ -2  0 11+  1  8  1
Curve Equation t Generators 31713a1 [0,-1,1,641,-7626] 1 [116:1270:1]
31713b (2 curves)	2	3+ 11+ 31-	-1 3+ -2 -2 11+  2  0 -2
Curve Equation t Generators 31713b1 [1,1,1,11,50] 2 [1:7:1]&[6:16:1] 31713b2 [1,1,1,-144,546] 2 [-14:14:1]&[-3:32:1]
31713c (1 curve)	0	3+ 11- 31+	-1 3+  3  2 11-  6  0  2
Curve Equation t 31713c1 [1,1,1,10551,150834] 1
31713d (2 curves)	1	3- 11+ 31-	1 3- -2 -2 11+ -4  2  6
Curve Equation t Generators 31713d1 [1,0,1,-96601182,-354439319621] 2 [30959449486615529182675107442:-1427830251272579575538892691851:2519318497389698040651224] 31713d2 [1,0,1,-239746937,940342663505] 2 [-345195400457133:-87494953268396677:60098096213]
31713e (4 curves)	1	3- 11+ 31-	1 3- -2  4 11+  2  2  0
Curve Equation t Generators 31713e1 [1,0,1,-6267,188809] 2 [1942:27855:8] 31713e2 [1,0,1,-11072,-141775] 4 [-2988:34957:64] 31713e3 [1,0,1,41783,-1093165] 2 [1165:39779:1] 31713e4 [1,0,1,-140807,-20328541] 2 [150064530:392493793:343000]
31713f (1 curve)	1	3- 11+ 31-	-1 3-  3  2 11+ -6  0  2
Curve Equation t Generators 31713f1 [1,0,0,11,-4] 1 [5:11:1]
31713g (1 curve)	0	3- 11- 31-	0 3- -2  0 11- -1 -8  1
Curve Equation t 31713g1 [0,1,1,615681,221020808] 1
31713h (2 curves)	0	3- 11- 31-	-1 3- -2 -2 11- -2  0 -2
Curve Equation t 31713h1 [1,0,0,10551,-1357680] 2 31713h2 [1,0,0,-138404,-18070431] 2

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

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