Elliptic curve search results

Results (22 matches)

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators	Manin constant
6440.b1	6440h1	6440.b	6440h	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{2} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1.342780211$	$1$		$5$	$1024$	$-0.040798$	$7086244/4025$	$0.89479$	$2.58887$	$[0, 1, 0, -40, 0]$	\(y^2=x^3+x^2-40x\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(8, 16)]$	$1$
12880.y1	12880k1	12880.y	12880k	$2$	$2$	\( 2^{4} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{2} \cdot 7 \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1$	$1$		$1$	$2048$	$-0.040798$	$7086244/4025$	$0.89479$	$2.39925$	$[0, -1, 0, -40, 0]$	\(y^2=x^3-x^2-40x\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[ ]$	$1$
32200.x1	32200j1	32200.x	32200j	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{8} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$4.366057963$	$1$		$1$	$24576$	$0.763921$	$7086244/4025$	$0.89479$	$3.11779$	$[0, -1, 0, -1008, 2012]$	\(y^2=x^3-x^2-1008x+2012\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(-227/3, 2800/3)]$	$1$
45080.bb1	45080u1	45080.bb	45080u	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{10} \cdot 5^{2} \cdot 7^{7} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$5.188185671$	$1$		$3$	$49152$	$0.932158$	$7086244/4025$	$0.89479$	$3.20828$	$[0, -1, 0, -1976, -3940]$	\(y^2=x^3-x^2-1976x-3940\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(3526, 209328)]$	$1$
51520.h1	51520by1	51520.h	51520by	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 5^{2} \cdot 7 \cdot 23 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$2.328428417$	$1$		$15$	$16384$	$0.305776$	$7086244/4025$	$0.89479$	$2.47601$	$[0, 1, 0, -161, -161]$	\(y^2=x^3+x^2-161x-161\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(15, 32), (-6, 25)]$	$1$
51520.cc1	51520f1	51520.cc	51520f	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 5^{2} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$2.472654148$	$1$		$3$	$16384$	$0.305776$	$7086244/4025$	$0.89479$	$2.47601$	$[0, -1, 0, -161, 161]$	\(y^2=x^3-x^2-161x+161\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(19, 60)]$	$1$
57960.j1	57960m1	57960.j	57960m	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$2.241885194$	$1$		$5$	$24576$	$0.508509$	$7086244/4025$	$0.89479$	$2.67124$	$[0, 0, 0, -363, -362]$	\(y^2=x^3-363x-362\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(-6, 40)]$	$1$
64400.d1	64400e1	64400.d	64400e	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 5^{8} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1.030332069$	$1$		$9$	$49152$	$0.763921$	$7086244/4025$	$0.89479$	$2.92262$	$[0, 1, 0, -1008, -2012]$	\(y^2=x^3+x^2-1008x-2012\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(48, 250)]$	$1$
90160.e1	90160t1	90160.e	90160t	$2$	$2$	\( 2^{4} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{10} \cdot 5^{2} \cdot 7^{7} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$0.570736000$	$1$		$9$	$98304$	$0.932158$	$7086244/4025$	$0.89479$	$3.01337$	$[0, 1, 0, -1976, 3940]$	\(y^2=x^3+x^2-1976x+3940\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(72, 490)]$	$1$
115920.bu1	115920u1	115920.bu	115920u	$2$	$2$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1.478516657$	$1$		$7$	$49152$	$0.508509$	$7086244/4025$	$0.89479$	$2.51245$	$[0, 0, 0, -363, 362]$	\(y^2=x^3-363x+362\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(19, 18)]$	$1$
148120.g1	148120h1	148120.g	148120h	$2$	$2$	\( 2^{3} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{10} \cdot 5^{2} \cdot 7 \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1$	$1$		$1$	$540672$	$1.526949$	$7086244/4025$	$0.89479$	$3.48722$	$[0, 1, 0, -21336, -170240]$	\(y^2=x^3+x^2-21336x-170240\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[ ]$	$1$
225400.q1	225400bq1	225400.q	225400bq	$2$	$2$	\( 2^{3} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{10} \cdot 5^{8} \cdot 7^{7} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$2.027392258$	$1$		$5$	$1179648$	$1.736876$	$7086244/4025$	$0.89479$	$3.57282$	$[0, 1, 0, -49408, -591312]$	\(y^2=x^3+x^2-49408x-591312\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(-68, 1568)]$	$1$
257600.bc1	257600bc1	257600.bc	257600bc	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 5^{8} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1.917361822$	$1$		$5$	$393216$	$1.110495$	$7086244/4025$	$0.89479$	$2.93123$	$[0, 1, 0, -4033, 12063]$	\(y^2=x^3+x^2-4033x+12063\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(-7, 200)]$	$1$
257600.ff1	257600ff1	257600.ff	257600ff	$2$	$2$	\( 2^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 5^{8} \cdot 7 \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1$	$1$		$1$	$393216$	$1.110495$	$7086244/4025$	$0.89479$	$2.93123$	$[0, -1, 0, -4033, -12063]$	\(y^2=x^3-x^2-4033x-12063\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[ ]$	$1$
289800.ds1	289800ds1	289800.ds	289800ds	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 23 \)	\( 2^{10} \cdot 3^{6} \cdot 5^{8} \cdot 7 \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1$	$1$		$1$	$589824$	$1.313227$	$7086244/4025$	$0.89479$	$3.09721$	$[0, 0, 0, -9075, -45250]$	\(y^2=x^3-9075x-45250\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[ ]$	$1$
296240.db1	296240db1	296240.db	296240db	$2$	$2$	\( 2^{4} \cdot 5 \cdot 7 \cdot 23^{2} \)	\( 2^{10} \cdot 5^{2} \cdot 7 \cdot 23^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1$	$1$		$1$	$1081344$	$1.526949$	$7086244/4025$	$0.89479$	$3.29537$	$[0, -1, 0, -21336, 170240]$	\(y^2=x^3-x^2-21336x+170240\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[ ]$	$1$
360640.bq1	360640bq1	360640.bq	360640bq	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{16} \cdot 5^{2} \cdot 7^{7} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$2.249015908$	$1$		$5$	$786432$	$1.278730$	$7086244/4025$	$0.89479$	$3.01192$	$[0, 1, 0, -7905, -39425]$	\(y^2=x^3+x^2-7905x-39425\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(93, 196)]$	$1$
360640.ig1	360640ig1	360640.ig	360640ig	$2$	$2$	\( 2^{6} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{16} \cdot 5^{2} \cdot 7^{7} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$3.355060501$	$1$		$3$	$786432$	$1.278730$	$7086244/4025$	$0.89479$	$3.01192$	$[0, -1, 0, -7905, 39425]$	\(y^2=x^3-x^2-7905x+39425\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(-85, 300)]$	$1$
405720.fe1	405720fe1	405720.fe	405720fe	$2$	$2$	\( 2^{3} \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 23 \)	\( 2^{10} \cdot 3^{6} \cdot 5^{2} \cdot 7^{7} \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$4.428571537$	$1$		$3$	$1179648$	$1.481462$	$7086244/4025$	$0.89479$	$3.17284$	$[0, 0, 0, -17787, 124166]$	\(y^2=x^3-17787x+124166\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(655, 16416)]$	$1$
450800.gb1	450800gb1	450800.gb	450800gb	$2$	$2$	\( 2^{4} \cdot 5^{2} \cdot 7^{2} \cdot 23 \)	\( 2^{10} \cdot 5^{8} \cdot 7^{7} \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1$	$1$		$1$	$2359296$	$1.736876$	$7086244/4025$	$0.89479$	$3.38259$	$[0, -1, 0, -49408, 591312]$	\(y^2=x^3-x^2-49408x+591312\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[ ]$	$1$
463680.iy1	463680iy1	463680.iy	463680iy	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$1$	$1$		$1$	$393216$	$0.855082$	$7086244/4025$	$0.89479$	$2.56425$	$[0, 0, 0, -1452, -2896]$	\(y^2=x^3-1452x-2896\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[ ]$	$1$
463680.mm1	463680mm1	463680.mm	463680mm	$2$	$2$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 23 \)	\( 2^{16} \cdot 3^{6} \cdot 5^{2} \cdot 7 \cdot 23 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	2.3.0.1	2B	$6440$	$12$	$0$	$2.892817389$	$1$		$5$	$393216$	$0.855082$	$7086244/4025$	$0.89479$	$2.56425$	$[0, 0, 0, -1452, 2896]$	\(y^2=x^3-1452x+2896\)	2.3.0.a.1, 40.6.0.d.1, 322.6.0.?, 6440.12.0.?	$[(-3, 85)]$	$1$

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