Learn more

Refine search


Results (1-50 of 436 matches)

Next   displayed columns for results
Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
2.1-a1 2.1-a \(\Q(\sqrt{129}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $29.18343844$ 2.569458482 \( -\frac{958464783206251}{2} a + \frac{5922266046113995}{2} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( -117348739 a - 607738365\) , \( 1649856442368 a + 8544455298751\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-117348739a-607738365\right){x}+1649856442368a+8544455298751$
2.1-a2 2.1-a \(\Q(\sqrt{129}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $29.18343844$ 2.569458482 \( -\frac{2651}{32} a + \frac{59835}{32} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 1311181 a + 6790485\) , \( -1010575092 a - 5233675779\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1311181a+6790485\right){x}-1010575092a-5233675779$
2.1-b1 2.1-b \(\Q(\sqrt{129}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $5.203755382$ $1.150939947$ 1.054641065 \( -\frac{958464783206251}{2} a + \frac{5922266046113995}{2} \) \( \bigl[a + 1\) , \( a\) , \( a\) , \( 731 a - 4419\) , \( 24963 a - 154005\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(731a-4419\right){x}+24963a-154005$
2.1-b2 2.1-b \(\Q(\sqrt{129}) \) \( 2 \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $1.040751076$ $28.77349869$ 1.054641065 \( -\frac{2651}{32} a + \frac{59835}{32} \) \( \bigl[a + 1\) , \( a\) , \( a\) , \( 11 a + 31\) , \( 23 a + 105\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(11a+31\right){x}+23a+105$
2.2-a1 2.2-a \(\Q(\sqrt{129}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $29.18343844$ 2.569458482 \( \frac{2651}{32} a + 1787 \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -1311181 a + 8101666\) , \( 1011886273 a - 6252352537\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1311181a+8101666\right){x}+1011886273a-6252352537$
2.2-a2 2.2-a \(\Q(\sqrt{129}) \) \( 2 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $29.18343844$ 2.569458482 \( \frac{958464783206251}{2} a + 2481900631453872 \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 117348739 a - 725087104\) , \( -1649973791107 a + 10195036828223\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(117348739a-725087104\right){x}-1649973791107a+10195036828223$
2.2-b1 2.2-b \(\Q(\sqrt{129}) \) \( 2 \) $1$ $\Z/5\Z$ $\mathrm{SU}(2)$ $1.040751076$ $28.77349869$ 1.054641065 \( \frac{2651}{32} a + 1787 \) \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 4 a + 10\) , \( 2 a + 6\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+10\right){x}+2a+6$
2.2-b2 2.2-b \(\Q(\sqrt{129}) \) \( 2 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $5.203755382$ $1.150939947$ 1.054641065 \( \frac{958464783206251}{2} a + 2481900631453872 \) \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -716 a - 3720\) , \( -28668 a - 148474\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-716a-3720\right){x}-28668a-148474$
4.1-a1 4.1-a \(\Q(\sqrt{129}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.151409674$ 4.386134892 \( -\frac{60716385}{64} a - \frac{19652787}{4} \) \( \bigl[1\) , \( a\) , \( a\) , \( -80 a + 505\) , \( 308288 a - 1904883\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-80a+505\right){x}+308288a-1904883$
4.1-a2 4.1-a \(\Q(\sqrt{129}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.151409674$ 4.386134892 \( \frac{60716385}{64} a - \frac{375160977}{64} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 79 a + 425\) , \( -308289 a - 1596595\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(79a+425\right){x}-308289a-1596595$
4.1-b1 4.1-b \(\Q(\sqrt{129}) \) \( 2^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.022799893$ $36.76371340$ 1.180802658 \( -\frac{60716385}{64} a - \frac{19652787}{4} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -16776 a - 86865\) , \( 2846099 a + 14739689\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-16776a-86865\right){x}+2846099a+14739689$
4.1-b2 4.1-b \(\Q(\sqrt{129}) \) \( 2^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.022799893$ $36.76371340$ 1.180802658 \( \frac{60716385}{64} a - \frac{375160977}{64} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 16775 a - 103641\) , \( -2846100 a + 17585788\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(16775a-103641\right){x}-2846100a+17585788$
4.2-a1 4.2-a \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.337287870$ $4.214438833$ 2.977289430 \( -6164480 a - 31924224 \) \( \bigl[0\) , \( -a\) , \( a\) , \( -393024 a + 2428472\) , \( 255241909 a - 1577116380\bigr] \) ${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(-393024a+2428472\right){x}+255241909a-1577116380$
4.2-b1 4.2-b \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.597796035$ $17.69503190$ 1.862685445 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( a\) , \( a + 11\) , \( -12145 a + 75047\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+11\right){x}-12145a+75047$
4.2-b2 4.2-b \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.199265345$ $17.69503190$ 1.862685445 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( a\) , \( a + 11\) , \( 905486 a + 4689425\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+11\right){x}+905486a+4689425$
4.2-c1 4.2-c \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.309179342$ $29.09037348$ 1.583780192 \( -6164480 a - 31924224 \) \( \bigl[0\) , \( -1\) , \( a\) , \( -259 a - 1341\) , \( 5493 a + 28441\bigr] \) ${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-259a-1341\right){x}+5493a+28441$
4.3-a1 4.3-a \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.337287870$ $4.214438833$ 2.977289430 \( 6164480 a - 38088704 \) \( \bigl[0\) , \( a - 1\) , \( a + 1\) , \( 393024 a + 2035448\) , \( -255241910 a - 1321874471\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(393024a+2035448\right){x}-255241910a-1321874471$
4.3-b1 4.3-b \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.597796035$ $17.69503190$ 1.862685445 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( a + 11\) , \( 12144 a + 62891\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+11\right){x}+12144a+62891$
4.3-b2 4.3-b \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $0.199265345$ $17.69503190$ 1.862685445 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( a + 11\) , \( -905487 a + 5594922\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+11\right){x}-905487a+5594922$
4.3-c1 4.3-c \(\Q(\sqrt{129}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.309179342$ $29.09037348$ 1.583780192 \( 6164480 a - 38088704 \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 259 a - 1600\) , \( -5494 a + 33934\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(259a-1600\right){x}-5494a+33934$
6.1-a1 6.1-a \(\Q(\sqrt{129}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.458701152$ $5.611992640$ 3.626369488 \( \frac{7198885}{432} a - \frac{911579}{9} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 1070 a - 6614\) , \( 46088 a - 284783\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1070a-6614\right){x}+46088a-284783$
6.1-b1 6.1-b \(\Q(\sqrt{129}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.032203325$ $20.75126785$ 1.412087948 \( \frac{7198885}{432} a - \frac{911579}{9} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 55114 a + 285435\) , \( -2721536 a - 14094588\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(55114a+285435\right){x}-2721536a-14094588$
6.2-a1 6.2-a \(\Q(\sqrt{129}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.458701152$ $5.611992640$ 3.626369488 \( -\frac{7198885}{432} a - \frac{36556907}{432} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1071 a - 5544\) , \( -46089 a - 238695\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1071a-5544\right){x}-46089a-238695$
6.2-b1 6.2-b \(\Q(\sqrt{129}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.032203325$ $20.75126785$ 1.412087948 \( -\frac{7198885}{432} a - \frac{36556907}{432} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( -55112 a + 340548\) , \( 2776649 a - 17156672\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-55112a+340548\right){x}+2776649a-17156672$
8.1-a1 8.1-a \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $4.348459975$ 3.828605526 \( -\frac{172032790985}{1073741824} a + \frac{30074625879}{33554432} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -2580396 a - 13363628\) , \( 23701425877 a + 122747512292\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-2580396a-13363628\right){x}+23701425877a+122747512292$
8.1-a2 8.1-a \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.348459975$ 3.828605526 \( \frac{1157415}{1024} a - \frac{220601}{32} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 284339 a + 1472572\) , \( -837230821 a - 4335941676\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(284339a+1472572\right){x}-837230821a-4335941676$
8.1-b1 8.1-b \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $2.078509084$ $15.94185712$ 1.944933359 \( \frac{2307}{2} a + 2608 \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -973 a - 5013\) , \( 34727 a + 179889\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-973a-5013\right){x}+34727a+179889$
8.1-b2 8.1-b \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $6.235527253$ $1.771317458$ 1.944933359 \( \frac{47232606203}{8} a - 36480294292 \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -17378 a - 89973\) , \( -2978637 a - 15426047\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-17378a-89973\right){x}-2978637a-15426047$
8.1-c1 8.1-c \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $29.10944917$ 2.562944090 \( \frac{2307}{2} a + 2608 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 10100 a - 62389\) , \( -1593582 a + 9846631\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(10100a-62389\right){x}-1593582a+9846631$
8.1-c2 8.1-c \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $29.10944917$ 2.562944090 \( \frac{47232606203}{8} a - 36480294292 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 869255 a - 5371029\) , \( -1049040548 a + 6481925431\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(869255a-5371029\right){x}-1049040548a+6481925431$
8.1-d1 8.1-d \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.911621126$ $2.188951422$ 1.473679633 \( -\frac{172032790985}{1073741824} a + \frac{30074625879}{33554432} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -524 a + 3249\) , \( -1696 a + 10502\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-524a+3249\right){x}-1696a+10502$
8.1-d2 8.1-d \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.637207042$ $19.70056279$ 1.473679633 \( \frac{1157415}{1024} a - \frac{220601}{32} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 91 a - 551\) , \( -980 a + 6078\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(91a-551\right){x}-980a+6078$
8.2-a1 8.2-a \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.348459975$ 3.828605526 \( -\frac{1157415}{1024} a - \frac{5901817}{1024} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -284341 a + 1756911\) , \( 837230820 a - 5173172497\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-284341a+1756911\right){x}+837230820a-5173172497$
8.2-a2 8.2-a \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $4.348459975$ 3.828605526 \( \frac{172032790985}{1073741824} a + \frac{790355237143}{1073741824} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 2580394 a - 15944024\) , \( -23701425878 a + 146448938169\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(2580394a-15944024\right){x}-23701425878a+146448938169$
8.2-b1 8.2-b \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $6.235527253$ $1.771317458$ 1.944933359 \( -\frac{47232606203}{8} a - \frac{244609748133}{8} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 17379 a - 107319\) , \( 2996015 a - 18512003\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(17379a-107319\right){x}+2996015a-18512003$
8.2-b2 8.2-b \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $2.078509084$ $15.94185712$ 1.944933359 \( -\frac{2307}{2} a + \frac{7523}{2} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 974 a - 5954\) , \( -33754 a + 208662\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(974a-5954\right){x}-33754a+208662$
8.2-c1 8.2-c \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $29.10944917$ 2.562944090 \( -\frac{47232606203}{8} a - \frac{244609748133}{8} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -869257 a - 4501774\) , \( 1049040547 a + 5432884883\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-869257a-4501774\right){x}+1049040547a+5432884883$
8.2-c2 8.2-c \(\Q(\sqrt{129}) \) \( 2^{3} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $29.10944917$ 2.562944090 \( -\frac{2307}{2} a + \frac{7523}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -10102 a - 52289\) , \( 1593581 a + 8253049\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10102a-52289\right){x}+1593581a+8253049$
8.2-d1 8.2-d \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.637207042$ $19.70056279$ 1.473679633 \( -\frac{1157415}{1024} a - \frac{5901817}{1024} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -93 a - 460\) , \( 979 a + 5098\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-93a-460\right){x}+979a+5098$
8.2-d2 8.2-d \(\Q(\sqrt{129}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.911621126$ $2.188951422$ 1.473679633 \( \frac{172032790985}{1073741824} a + \frac{790355237143}{1073741824} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 522 a + 2725\) , \( 1695 a + 8806\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(522a+2725\right){x}+1695a+8806$
10.2-a1 10.2-a \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $9.391352793$ 4.961175046 \( \frac{25965603}{31250} a - \frac{52921296}{15625} \) \( \bigl[a\) , \( a\) , \( 1\) , \( 102948240 a - 636107660\) , \( 1499528208294 a - 9265447360847\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(102948240a-636107660\right){x}+1499528208294a-9265447360847$
10.2-a2 10.2-a \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $9.391352793$ 4.961175046 \( \frac{1616685723}{200} a + \frac{1046625516}{25} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( -a + 9\) , \( -6 a - 23\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-a+9\right){x}-6a-23$
10.2-b1 10.2-b \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $17.47376826$ 0.769239755 \( -\frac{31939}{50} a + \frac{98673}{25} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -9 a - 44\) , \( -6443 a - 33372\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-9a-44\right){x}-6443a-33372$
10.2-b2 10.2-b \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $17.47376826$ 0.769239755 \( \frac{106969}{20} a + \frac{139871}{5} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 10\) , \( -a + 1\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+10{x}-a+1$
10.2-c1 10.2-c \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.124606412$ $5.853140175$ 2.318219832 \( \frac{6711461587}{204800} a + \frac{1085736051}{6400} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 82977 a - 512680\) , \( 156511178 a - 967068192\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(82977a-512680\right){x}+156511178a-967068192$
10.2-d1 10.2-d \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.023688676$ $23.63894871$ 2.563760464 \( \frac{6711461587}{204800} a + \frac{1085736051}{6400} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -807 a - 4157\) , \( 26887 a + 139262\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-807a-4157\right){x}+26887a+139262$
10.2-e1 10.2-e \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $42.75671159$ 1.882259273 \( -\frac{31939}{50} a + \frac{98673}{25} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 11246 a - 69472\) , \( -1333517 a + 8239667\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11246a-69472\right){x}-1333517a+8239667$
10.2-e2 10.2-e \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $42.75671159$ 1.882259273 \( \frac{106969}{20} a + \frac{139871}{5} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -17574147 a + 108589040\) , \( -219640655600 a + 1357139479951\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-17574147a+108589040\right){x}-219640655600a+1357139479951$
10.2-f1 10.2-f \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.067772993$ $26.27860898$ 1.254452365 \( \frac{25965603}{31250} a - \frac{52921296}{15625} \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( -1\) , \( 1\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}-{x}+1$
10.2-f2 10.2-f \(\Q(\sqrt{129}) \) \( 2 \cdot 5 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.067772993$ $26.27860898$ 1.254452365 \( \frac{1616685723}{200} a + \frac{1046625516}{25} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -73978694 a + 457107630\) , \( 132250044861 a - 817160905793\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-73978694a+457107630\right){x}+132250044861a-817160905793$
Next   displayed columns for results

  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.