Elliptic curve search results

Results (24 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
762.f1	762g2	762.f	762g	$2$	$7$	\( 2 \cdot 3 \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$	✓		$7$	7.48.0.5	7B.1.3	$7112$	$96$	$2$	$1$	$1$		$0$	$25872$	$2.686474$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$9.40063$	$[1, 0, 0, -22361106, -40701264948]$	\(y^2+xy=x^3-22361106x-40701264948\)	7.48.0-7.a.2.2, 1016.2.0.?, 7112.96.2.?	$[]$
2286.f1	2286f2	2286.f	2286f	$2$	$7$	\( 2 \cdot 3^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{8} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$21336$	$96$	$2$	$1.150157925$	$1$		$0$	$206976$	$3.235779$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$8.91761$	$[1, -1, 0, -201249954, 1098934153596]$	\(y^2+xy=x^3-x^2-201249954x+1098934153596\)	7.24.0.a.2, 21.48.0-7.a.2.2, 1016.2.0.?, 7112.48.2.?, 21336.96.2.?	$[(192891/5, 8735496/5)]$
6096.d1	6096f2	6096.d	6096f	$2$	$7$	\( 2^{4} \cdot 3 \cdot 127 \)	\( 2^{15} \cdot 3^{2} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$7112$	$96$	$2$	$1$	$1$		$0$	$620928$	$3.379620$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$8.11207$	$[0, -1, 0, -357777696, 2604880956672]$	\(y^2=x^3-x^2-357777696x+2604880956672\)	7.24.0.a.2, 28.48.0-7.a.2.1, 1016.2.0.?, 7112.96.2.?	$[]$
18288.s1	18288v2	18288.s	18288v	$2$	$7$	\( 2^{4} \cdot 3^{2} \cdot 127 \)	\( 2^{15} \cdot 3^{8} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$21336$	$96$	$2$	$36.20203506$	$1$		$0$	$4967424$	$3.928928$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.87564$	$[0, 0, 0, -3219999267, -70328565830878]$	\(y^2=x^3-3219999267x-70328565830878\)	7.24.0.a.2, 84.48.0.?, 1016.2.0.?, 7112.48.2.?, 21336.96.2.?	$[(-3760184105237959559/10712779, 1287270738749686372499376/10712779)]$
19050.c1	19050b2	19050.c	19050b	$2$	$7$	\( 2 \cdot 3 \cdot 5^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 5^{6} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$35560$	$96$	$2$	$53.43504968$	$1$		$0$	$3622080$	$3.491192$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.31000$	$[1, 1, 0, -559027650, -5087658118500]$	\(y^2+xy=x^3+x^2-559027650x-5087658118500\)	7.24.0.a.2, 35.48.0-7.a.2.1, 1016.2.0.?, 7112.48.2.?, 35560.96.2.?	$[(-9839146501858788397605681/26848515991, 135157294989940278865479211419287325/26848515991)]$
24384.n1	24384j2	24384.n	24384j	$2$	$7$	\( 2^{6} \cdot 3 \cdot 127 \)	\( 2^{21} \cdot 3^{2} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$7112$	$96$	$2$	$1$	$1$		$0$	$4967424$	$3.726196$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.41052$	$[0, -1, 0, -1431110785, -20837616542591]$	\(y^2=x^3-x^2-1431110785x-20837616542591\)	7.24.0.a.2, 56.48.0-7.a.2.1, 1016.2.0.?, 3556.48.0.?, 7112.96.2.?	$[]$
24384.bj1	24384bi2	24384.bj	24384bi	$2$	$7$	\( 2^{6} \cdot 3 \cdot 127 \)	\( 2^{21} \cdot 3^{2} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$7112$	$96$	$2$	$18.89964979$	$1$		$0$	$4967424$	$3.726196$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.41052$	$[0, 1, 0, -1431110785, 20837616542591]$	\(y^2=x^3+x^2-1431110785x+20837616542591\)	7.24.0.a.2, 56.48.0-7.a.2.2, 1016.2.0.?, 1778.48.0.?, 7112.96.2.?	$[(4321144265/451, 13939986955296/451)]$
37338.n1	37338q2	37338.n	37338q	$2$	$7$	\( 2 \cdot 3 \cdot 7^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 7^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.48.0.2	7B.1.4	$7112$	$96$	$2$	$1$	$1$		$0$	$9779616$	$3.659428$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.03450$	$[1, 1, 1, -1095694195, 13959438182969]$	\(y^2+xy+y=x^3+x^2-1095694195x+13959438182969\)	7.48.0-7.a.2.1, 1016.2.0.?, 7112.96.2.?	$[]$
57150.bi1	57150bl2	57150.bi	57150bl	$2$	$7$	\( 2 \cdot 3^{2} \cdot 5^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{8} \cdot 5^{6} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$106680$	$96$	$2$	$19.70024826$	$1$		$0$	$28976640$	$4.040497$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.17861$	$[1, -1, 1, -5031248855, 137361737950647]$	\(y^2+xy+y=x^3-x^2-5031248855x+137361737950647\)	7.24.0.a.2, 105.48.0.?, 1016.2.0.?, 7112.48.2.?, 106680.96.2.?	$[(41471073905/1007, -961734671232/1007)]$
73152.bf1	73152cp2	73152.bf	73152cp	$2$	$7$	\( 2^{6} \cdot 3^{2} \cdot 127 \)	\( 2^{21} \cdot 3^{8} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$21336$	$96$	$2$	$40.95686356$	$1$		$0$	$39739392$	$4.275497$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.27217$	$[0, 0, 0, -12879997068, -562628526647024]$	\(y^2=x^3-12879997068x-562628526647024\)	7.24.0.a.2, 168.48.0.?, 1016.2.0.?, 5334.48.0.?, 7112.48.2.?, $\ldots$	$[(-291095443555229390654/66657225, 280901778756971498372366144/66657225)]$
73152.bm1	73152bn2	73152.bm	73152bn	$2$	$7$	\( 2^{6} \cdot 3^{2} \cdot 127 \)	\( 2^{21} \cdot 3^{8} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$21336$	$96$	$2$	$4.649046289$	$1$		$0$	$39739392$	$4.275497$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.27217$	$[0, 0, 0, -12879997068, 562628526647024]$	\(y^2=x^3-12879997068x+562628526647024\)	7.24.0.a.2, 168.48.0.?, 1016.2.0.?, 7112.48.2.?, 10668.48.0.?, $\ldots$	$[(3157981/7, 163015803/7)]$
92202.k1	92202l2	92202.k	92202l	$2$	$7$	\( 2 \cdot 3 \cdot 11^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 11^{6} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$78232$	$96$	$2$	$32.62282392$	$1$		$0$	$30787680$	$3.885422$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.71547$	$[1, 0, 1, -2705693829, 54170677951960]$	\(y^2+xy+y=x^3-2705693829x+54170677951960\)	7.24.0.a.2, 77.48.0.?, 1016.2.0.?, 7112.48.2.?, 78232.96.2.?	$[(439634326766186/138535, 5425651888435793422386/138535)]$
96774.h1	96774h2	96774.h	96774h	$2$	$7$	\( 2 \cdot 3 \cdot 127^{2} \)	\( 2^{3} \cdot 3^{2} \cdot 127^{13} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$7112$	$96$	$2$	$17.06957129$	$1$		$0$	$417263616$	$5.108566$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.96569$	$[1, 1, 1, -360662279010, 83367811912911159]$	\(y^2+xy+y=x^3+x^2-360662279010x+83367811912911159\)	7.24.0.a.2, 56.48.0-7.a.2.6, 889.48.0.?, 1016.2.0.?, 7112.96.2.?	$[(-15448742673341/8239, 219296703224578556807/8239)]$
112014.e1	112014l2	112014.e	112014l	$2$	$7$	\( 2 \cdot 3^{2} \cdot 7^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{8} \cdot 7^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$21336$	$96$	$2$	$1$	$1$		$0$	$78236928$	$4.208733$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.93675$	$[1, -1, 0, -9861247755, -376914692187923]$	\(y^2+xy=x^3-x^2-9861247755x-376914692187923\)	7.24.0.a.2, 21.48.0-7.a.2.1, 1016.2.0.?, 7112.48.2.?, 21336.96.2.?	$[]$
128778.k1	128778m2	128778.k	128778m	$2$	$7$	\( 2 \cdot 3 \cdot 13^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 13^{6} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$92456$	$96$	$2$	$10.01442218$	$1$		$0$	$60850944$	$3.968948$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.60996$	$[1, 0, 1, -3779026918, -89416900063840]$	\(y^2+xy+y=x^3-3779026918x-89416900063840\)	7.24.0.a.2, 91.48.0.?, 1016.2.0.?, 7112.48.2.?, 92456.96.2.?	$[(-10257816/17, 93945008/17)]$
152400.bw1	152400x2	152400.bw	152400x	$2$	$7$	\( 2^{4} \cdot 3 \cdot 5^{2} \cdot 127 \)	\( 2^{15} \cdot 3^{2} \cdot 5^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$35560$	$96$	$2$	$1$	$1$		$0$	$86929920$	$4.184341$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.73326$	$[0, 1, 0, -8944442408, 325592230699188]$	\(y^2=x^3+x^2-8944442408x+325592230699188\)	7.24.0.a.2, 140.48.0.?, 1016.2.0.?, 7112.48.2.?, 35560.96.2.?	$[]$
220218.t1	220218p2	220218.t	220218p	$2$	$7$	\( 2 \cdot 3 \cdot 17^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 17^{6} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$120904$	$96$	$2$	$11.29971291$	$1$		$0$	$130394880$	$4.103081$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.45253$	$[1, 1, 1, -6462359640, -199958852329887]$	\(y^2+xy+y=x^3+x^2-6462359640x-199958852329887\)	7.24.0.a.2, 119.48.0.?, 1016.2.0.?, 7112.48.2.?, 120904.96.2.?	$[(-7844717/13, 53296049/13)]$
275082.c1	275082c2	275082.c	275082c	$2$	$7$	\( 2 \cdot 3 \cdot 19^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 19^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$135128$	$96$	$2$	$1$	$9$	$3$	$0$	$185812704$	$4.158691$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.39121$	$[1, 1, 0, -8072359273, 279153831559789]$	\(y^2+xy=x^3+x^2-8072359273x+279153831559789\)	7.24.0.a.2, 133.48.0.?, 1016.2.0.?, 7112.48.2.?, 135128.96.2.?	$[]$
276606.bo1	276606bo2	276606.bo	276606bo	$2$	$7$	\( 2 \cdot 3^{2} \cdot 11^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{8} \cdot 11^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$234696$	$96$	$2$	$1$	$49$	$7$	$0$	$246301440$	$4.434731$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.65274$	$[1, -1, 1, -24351244457, -1462608304702927]$	\(y^2+xy+y=x^3-x^2-24351244457x-1462608304702927\)	7.24.0.a.2, 231.48.0.?, 1016.2.0.?, 7112.48.2.?, 234696.96.2.?	$[]$
290322.g1	290322g2	290322.g	290322g	$2$	$7$	\( 2 \cdot 3^{2} \cdot 127^{2} \)	\( 2^{3} \cdot 3^{8} \cdot 127^{13} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$21336$	$96$	$2$	$116.0629474$	$1$		$0$	$3338108928$	$5.657875$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$7.79401$	$[1, -1, 0, -3245960511090, -2250934167609112388]$	\(y^2+xy=x^3-x^2-3245960511090x-2250934167609112388\)	7.24.0.a.2, 168.48.0.?, 1016.2.0.?, 2667.48.0.?, 7112.48.2.?, $\ldots$	$[(-16441056479992707849756334614090019603317130260958789733419/125726549183655046173403285, 644991126051420087490110134747747128980761688242805147811747976728243981361200084349/125726549183655046173403285)]$
298704.bq1	298704bq2	298704.bq	298704bq	$2$	$7$	\( 2^{4} \cdot 3 \cdot 7^{2} \cdot 127 \)	\( 2^{15} \cdot 3^{2} \cdot 7^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$7112$	$96$	$2$	$1$	$49$	$7$	$0$	$234710784$	$4.352577$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.53399$	$[0, 1, 0, -17531107120, -893439105924268]$	\(y^2=x^3+x^2-17531107120x-893439105924268\)	7.24.0.a.2, 28.48.0-7.a.2.2, 1016.2.0.?, 7112.96.2.?	$[]$
386334.bm1	386334bm2	386334.bm	386334bm	$2$	$7$	\( 2 \cdot 3^{2} \cdot 13^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{8} \cdot 13^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$277368$	$96$	$2$	$1$	$1$		$0$	$486807552$	$4.518257$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.55787$	$[1, -1, 1, -34011242258, 2414256301723673]$	\(y^2+xy+y=x^3-x^2-34011242258x+2414256301723673\)	7.24.0.a.2, 273.48.0.?, 1016.2.0.?, 7112.48.2.?, 277368.96.2.?	$[]$
403098.y1	403098y2	403098.y	403098y	$2$	$7$	\( 2 \cdot 3 \cdot 23^{2} \cdot 127 \)	\( 2^{3} \cdot 3^{2} \cdot 23^{6} \cdot 127^{7} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$163576$	$96$	$2$	$7.064446448$	$1$		$2$	$322727328$	$4.254219$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.29081$	$[1, 0, 0, -11829025085, 495188632572153]$	\(y^2+xy=x^3-11829025085x+495188632572153\)	7.24.0.a.2, 161.48.0.?, 1016.2.0.?, 7112.48.2.?, 163576.96.2.?	$[(62608, 48997)]$
457200.dt1	457200dt2	457200.dt	457200dt	$2$	$7$	\( 2^{4} \cdot 3^{2} \cdot 5^{2} \cdot 127 \)	\( 2^{15} \cdot 3^{8} \cdot 5^{6} \cdot 127^{7} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$7$	7.24.0.2	7B.6.3	$106680$	$96$	$2$	$1$	$9$	$3$	$0$	$695439360$	$4.733643$	$1236526859255318155975783969/38367061931916216$	$1.06416$	$6.67145$	$[0, 0, 0, -80499981675, -8791070728859750]$	\(y^2=x^3-80499981675x-8791070728859750\)	7.24.0.a.2, 420.48.0.?, 1016.2.0.?, 7112.48.2.?, 106680.96.2.?	$[]$

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