Elliptic curve search results

Conductor	j-invariant	Rank	Torsion	Complex multiplication
Bad$\ p$	Discriminant	Regulator	Analytic order of Ш	Galois image
Isogeny class size	Isogeny class degree	Cyclic isogeny degree	$p\ $div$\ $|Ш|	Nonmax$\ \ell$
Curves per isogeny class	Reduction	Integral points	Faltings height

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Results (21 matches)

 

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	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	Weierstrass coefficients	Weierstrass equation
3990.bb4	3990bb1	3990.bb	3990bb	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{6} \cdot 5 \cdot 7 \cdot 19 \)	$0$	$\Z/4\Z$	$\Q$		$\mathrm{SU}(2)$	✓		$2$	8.24.0.45	2B	$1$	$1$		$3$	$7680$	$0.840460$	$114113060120923921/124104960$	$[1, 0, 0, -10105, 390137]$	\(y^2+xy=x^3-10105x+390137\)
11970.c4	11970r1	11970.c	11970r	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.11	2B	$1$	$4$	$2$	$1$	$61440$	$1.389765$	$114113060120923921/124104960$	$[1, -1, 0, -90945, -10533699]$	\(y^2+xy=x^3-x^2-90945x-10533699\)
19950.o4	19950g1	19950.o	19950g	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{6} \cdot 5^{7} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$1$	$1$		$1$	$184320$	$1.645178$	$114113060120923921/124104960$	$[1, 1, 0, -252625, 48767125]$	\(y^2+xy=x^3+x^2-252625x+48767125\)
27930.ci4	27930cg1	27930.ci	27930cg	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{6} \cdot 5 \cdot 7^{7} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$1$	$1$		$1$	$368640$	$1.813414$	$114113060120923921/124104960$	$[1, 1, 1, -495146, -134312137]$	\(y^2+xy+y=x^3+x^2-495146x-134312137\)
31920.ba4	31920bk1	31920.ba	31920bk	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{20} \cdot 3^{6} \cdot 5 \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.55	2B	$11.72712135$	$1$		$1$	$184320$	$1.533607$	$114113060120923921/124104960$	$[0, -1, 0, -161680, -24968768]$	\(y^2=x^3-x^2-161680x-24968768\)
59850.fe4	59850fh1	59850.fe	59850fh	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{8} \cdot 3^{12} \cdot 5^{7} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$1$	$1$		$1$	$1474560$	$2.194485$	$114113060120923921/124104960$	$[1, -1, 1, -2273630, -1318986003]$	\(y^2+xy+y=x^3-x^2-2273630x-1318986003\)
75810.x4	75810w1	75810.x	75810w	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 5 \cdot 7 \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.9	2B	$16.55061398$	$1$		$1$	$2764800$	$2.312679$	$114113060120923921/124104960$	$[1, 1, 0, -3647912, -2683245504]$	\(y^2+xy=x^3+x^2-3647912x-2683245504\)
83790.bi4	83790cn1	83790.bi	83790cn	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{12} \cdot 5 \cdot 7^{7} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$6.256739012$	$1$		$3$	$2949120$	$2.362720$	$114113060120923921/124104960$	$[1, -1, 0, -4456314, 3621971380]$	\(y^2+xy=x^3-x^2-4456314x+3621971380\)
95760.cu4	95760ea1	95760.cu	95760ea	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{20} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.11	2B	$7.906970545$	$1$		$1$	$1474560$	$2.082912$	$114113060120923921/124104960$	$[0, 0, 0, -1455123, 675611858]$	\(y^2=x^3-1455123x+675611858\)
127680.d4	127680j1	127680.d	127680j	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{6} \cdot 5 \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.97	2B	$1$	$1$		$1$	$1474560$	$1.880180$	$114113060120923921/124104960$	$[0, -1, 0, -646721, 200396865]$	\(y^2=x^3-x^2-646721x+200396865\)
127680.ew4	127680fi1	127680.ew	127680fi	$6$	$8$	\( 2^{6} \cdot 3 \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{6} \cdot 5 \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.95	2B	$1$	$4$	$2$	$1$	$1474560$	$1.880180$	$114113060120923921/124104960$	$[0, 1, 0, -646721, -200396865]$	\(y^2=x^3+x^2-646721x-200396865\)
139650.ef4	139650ha1	139650.ef	139650ha	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{6} \cdot 5^{7} \cdot 7^{7} \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.14	2B	$1$	$1$		$1$	$8847360$	$2.618134$	$114113060120923921/124104960$	$[1, 0, 1, -12378651, -16764259802]$	\(y^2+xy+y=x^3-12378651x-16764259802\)
159600.do4	159600bt1	159600.do	159600bt	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{20} \cdot 3^{6} \cdot 5^{7} \cdot 7 \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$10.90968063$	$1$		$11$	$4423680$	$2.338326$	$114113060120923921/124104960$	$[0, 1, 0, -4042008, -3129180012]$	\(y^2=x^3+x^2-4042008x-3129180012\)
223440.dt4	223440bv1	223440.dt	223440bv	$6$	$8$	\( 2^{4} \cdot 3 \cdot 5 \cdot 7^{2} \cdot 19 \)	\( 2^{20} \cdot 3^{6} \cdot 5 \cdot 7^{7} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$2.085217768$	$1$		$19$	$8847360$	$2.506561$	$114113060120923921/124104960$	$[0, 1, 0, -7922336, 8580132084]$	\(y^2=x^3+x^2-7922336x+8580132084\)
227430.dg4	227430bq1	227430.dg	227430bq	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 19^{7} \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.87	2B	$1$	$1$		$1$	$22118400$	$2.861984$	$114113060120923921/124104960$	$[1, -1, 1, -32831213, 72414797397]$	\(y^2+xy+y=x^3-x^2-32831213x+72414797397\)
379050.kd4	379050kd1	379050.kd	379050kd	$6$	$8$	\( 2 \cdot 3 \cdot 5^{2} \cdot 7 \cdot 19^{2} \)	\( 2^{8} \cdot 3^{6} \cdot 5^{7} \cdot 7 \cdot 19^{7} \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$9.114803904$	$1$		$1$	$66355200$	$3.117397$	$114113060120923921/124104960$	$[1, 0, 0, -91197813, -335223292383]$	\(y^2+xy=x^3-91197813x-335223292383\)
383040.ki4	383040ki1	383040.ki	383040ki	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$1$	$16$	$2$	$1$	$11796480$	$2.429485$	$114113060120923921/124104960$	$[0, 0, 0, -5820492, -5404894864]$	\(y^2=x^3-5820492x-5404894864\)
383040.lp4	383040lp1	383040.lp	383040lp	$6$	$8$	\( 2^{6} \cdot 3^{2} \cdot 5 \cdot 7 \cdot 19 \)	\( 2^{26} \cdot 3^{12} \cdot 5 \cdot 7 \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	16.24.0.4	2B	$8.216601817$	$1$		$1$	$11796480$	$2.429485$	$114113060120923921/124104960$	$[0, 0, 0, -5820492, 5404894864]$	\(y^2=x^3-5820492x+5404894864\)
418950.ko4	418950ko1	418950.ko	418950ko	$6$	$8$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{12} \cdot 5^{7} \cdot 7^{7} \cdot 19 \)	$1$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.24.0.87	2B	$2.643772617$	$1$		$5$	$70778880$	$3.167439$	$114113060120923921/124104960$	$[1, -1, 1, -111407855, 452635014647]$	\(y^2+xy+y=x^3-x^2-111407855x+452635014647\)
478800.gk4	478800gk1	478800.gk	478800gk	$6$	$8$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 7 \cdot 19 \)	\( 2^{20} \cdot 3^{12} \cdot 5^{7} \cdot 7 \cdot 19 \)	$0$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$1$	$1$		$1$	$35389440$	$2.887630$	$114113060120923921/124104960$	$[0, 0, 0, -36378075, 84451482250]$	\(y^2=x^3-36378075x+84451482250\)
482790.dr4	482790dr1	482790.dr	482790dr	$6$	$8$	\( 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \cdot 19 \)	\( 2^{8} \cdot 3^{6} \cdot 5 \cdot 7 \cdot 11^{6} \cdot 19 \)	$2$	$\Z/2\Z$	$\Q$		$\mathrm{SU}(2)$			$2$	8.12.0.5	2B	$9.376272649$	$1$		$13$	$9830400$	$2.039406$	$114113060120923921/124104960$	$[1, 0, 1, -1222708, -520495054]$	\(y^2+xy+y=x^3-1222708x-520495054\)