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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
4.2-a1 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.813617215$ 0.609156265 \( -\frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} + 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 5 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -986 a^{3} + 2462 a^{2} + 7270 a - 5617\) , \( -24055 a^{3} + 130017 a^{2} + 277176 a - 233563\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{3}-5a+1\right){x}^{2}+\left(-986a^{3}+2462a^{2}+7270a-5617\right){x}-24055a^{3}+130017a^{2}+277176a-233563$
4.2-a2 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.813617215$ 0.609156265 \( \frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} - 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) \( \bigl[a^{2} + a - 3\) , \( a^{3} - 4 a + 1\) , \( a^{3} - 4 a\) , \( 993 a^{3} + 2463 a^{2} - 7301 a - 5617\) , \( 20899 a^{3} + 125700 a^{2} - 259626 a - 220971\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}-4a+1\right){x}^{2}+\left(993a^{3}+2463a^{2}-7301a-5617\right){x}+20899a^{3}+125700a^{2}-259626a-220971$
4.2-a3 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.508937725$ 0.609156265 \( -\frac{653762688677050897}{64} a^{2} + \frac{1491086515722280627}{32} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 981 a^{2} - 4478\) , \( 23629 a^{2} - 107786\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(981a^{2}-4478\right){x}+23629a^{2}-107786$
4.2-a4 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $65.90299447$ 0.609156265 \( -179213540276326839556 a^{3} + 382760552527098253312 a^{2} + \frac{157151345464271319581}{2} a - 167820287562717580568 \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 145 a^{3} + 91 a^{2} - 645 a - 453\) , \( 1478 a^{3} + 1064 a^{2} - 6784 a - 4764\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(145a^{3}+91a^{2}-645a-453\right){x}+1478a^{3}+1064a^{2}-6784a-4764$
4.2-a5 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $65.90299447$ 0.609156265 \( 179213540276326839556 a^{3} + 382760552527098253312 a^{2} - \frac{157151345464271319581}{2} a - 167820287562717580568 \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( -145 a^{3} + 91 a^{2} + 645 a - 453\) , \( -1478 a^{3} + 1064 a^{2} + 6784 a - 4764\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-145a^{3}+91a^{2}+645a-453\right){x}-1478a^{3}+1064a^{2}+6784a-4764$
4.2-a6 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.03575090$ 0.609156265 \( -\frac{203862548967}{4096} a^{2} + \frac{464995782961}{2048} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 61 a^{2} - 278\) , \( 349 a^{2} - 1594\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(61a^{2}-278\right){x}+349a^{2}-1594$
4.2-a7 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $527.2239557$ 0.609156265 \( \frac{54503407609}{4} a^{2} - 5973867768 \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( 11 a^{2} - 53\) , \( 28 a^{2} - 128\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(11a^{2}-53\right){x}+28a^{2}-128$
4.2-a8 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2108.895823$ 0.609156265 \( \frac{915957}{16} a^{2} - \frac{186929}{8} \) \( \bigl[1\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( a^{2} - 3\) , \( 0\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(a^{2}-3\right){x}$
4.2-a9 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $527.2239557$ 0.609156265 \( \frac{110887}{256} a^{2} - \frac{64929}{256} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( a^{2} - 5\) , \( -4 a^{2} + 18\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a^{2}-5\right){x}-4a^{2}+18$
4.2-a10 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.508937725$ 0.609156265 \( \frac{55573026649}{16777216} a^{2} - \frac{126228971439}{8388608} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 9 a^{2} - 5\) , \( -106 a^{2} + 46\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(9a^{2}-5\right){x}-106a^{2}+46$
4.2-a11 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $527.2239557$ 0.609156265 \( -\frac{110887}{256} a^{2} + \frac{244753}{128} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -a^{2}\) , \( 4 a^{2} - 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a^{2}{x}+4a^{2}-2$
4.2-a12 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.508937725$ 0.609156265 \( -\frac{55573026649}{16777216} a^{2} + \frac{25407190367}{16777216} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -9 a^{2} + 40\) , \( 106 a^{2} - 484\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-9a^{2}+40\right){x}+106a^{2}-484$
4.2-a13 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $527.2239557$ 0.609156265 \( -\frac{54503407609}{4} a^{2} + \frac{248621566973}{4} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -12 a^{2} + 4\) , \( -28 a^{2} + 12\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-12a^{2}+4\right){x}-28a^{2}+12$
4.2-a14 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2108.895823$ 0.609156265 \( -\frac{915957}{16} a^{2} + \frac{4205927}{16} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -2 a^{2} + 4\) , \( 0\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-2a^{2}+4\right){x}$
4.2-a15 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.03575090$ 0.609156265 \( \frac{203862548967}{4096} a^{2} - \frac{89321178913}{4096} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -62 a^{2} + 29\) , \( -349 a^{2} + 151\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-62a^{2}+29\right){x}-349a^{2}+151$
4.2-a16 4.2-a 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.508937725$ 0.609156265 \( \frac{653762688677050897}{64} a^{2} - \frac{286640411940693231}{64} \) \( \bigl[1\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -982 a^{2} + 429\) , \( -23629 a^{2} + 10359\bigr] \) ${y}^2+{x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-982a^{2}+429\right){x}-23629a^{2}+10359$
4.2-b1 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.235926723$ 2.826218305 \( -\frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} + 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( 491 a^{3} - 384 a^{2} - 915 a - 356\) , \( 9226 a^{3} - 16357 a^{2} - 12726 a + 1248\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(491a^{3}-384a^{2}-915a-356\right){x}+9226a^{3}-16357a^{2}-12726a+1248$
4.2-b2 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.235926723$ 2.826218305 \( \frac{2598999057507859430840814142230563}{8} a^{3} - 215117023039975647450343147847680 a^{2} - 1481933932657809377628672524686862 a + 981267661531062863922029372621544 \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( -489 a^{3} - 384 a^{2} + 905 a - 356\) , \( -9226 a^{3} - 16357 a^{2} + 12726 a + 1248\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(-489a^{3}-384a^{2}+905a-356\right){x}-9226a^{3}-16357a^{2}+12726a+1248$
4.2-b3 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.774827576$ 2.826218305 \( -\frac{653762688677050897}{64} a^{2} + \frac{1491086515722280627}{32} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 64 a^{2} - 5 a - 36\) , \( -437 a^{2} + 16\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-64a^{2}-5a-36\right){x}-437a^{2}+16$
4.2-b4 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $543.5751710$ 2.826218305 \( \frac{915957}{16} a^{2} - \frac{186929}{8} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 4 a^{2} - 5 a - 1\) , \( -10 a^{2} + 3\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-4a^{2}-5a-1\right){x}-10a^{2}+3$
4.2-b5 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $60.39724122$ 2.826218305 \( -\frac{203862548967}{4096} a^{2} + \frac{464995782961}{2048} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 24 a^{2} - 5 a + 4\) , \( 83 a^{2} - 40\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-24a^{2}-5a+4\right){x}+83a^{2}-40$
4.2-b6 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $33.97344818$ 2.826218305 \( \frac{54503407609}{4} a^{2} - 5973867768 \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 4\) , \( a^{3} - 4 a\) , \( a^{3} - 74 a^{2} - 5 a + 29\) , \( -544 a^{2} + 237\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-4\right){x}^{2}+\left(a^{3}-74a^{2}-5a+29\right){x}-544a^{2}+237$
4.2-b7 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $241.5889648$ 2.826218305 \( \frac{653762688677050897}{64} a^{2} - \frac{286640411940693231}{64} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 66 a^{2} - 5 a - 359\) , \( -372 a^{2} + 1811\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+66a^{2}-5a-359\right){x}-372a^{2}+1811$
4.2-b8 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $2174.300684$ 2.826218305 \( -\frac{54503407609}{4} a^{2} + \frac{248621566973}{4} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 76 a^{2} - 5 a - 344\) , \( -469 a^{2} + 2140\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+76a^{2}-5a-344\right){x}-469a^{2}+2140$
4.2-b9 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $241.5889648$ 2.826218305 \( \frac{203862548967}{4096} a^{2} - \frac{89321178913}{4096} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 26 a^{2} - 5 a - 119\) , \( 108 a^{2} - 493\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+26a^{2}-5a-119\right){x}+108a^{2}-493$
4.2-b10 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z\oplus\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $2174.300684$ 2.826218305 \( -\frac{915957}{16} a^{2} + \frac{4205927}{16} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} + a^{2} - 5 a - 2\) , \( a^{3} - 4 a\) , \( a^{3} + 6 a^{2} - 5 a - 24\) , \( -5 a^{2} + 24\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(a^{3}+a^{2}-5a-2\right){x}^{2}+\left(a^{3}+6a^{2}-5a-24\right){x}-5a^{2}+24$
4.2-b11 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $15.09931030$ 2.826218305 \( \frac{55573026649}{16777216} a^{2} - \frac{126228971439}{8388608} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2 a^{3} + 10 a^{2} - 10 a - 47\) , \( a^{3} + 30 a^{2} - 5 a - 137\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(2a^{3}+10a^{2}-10a-47\right){x}+a^{3}+30a^{2}-5a-137$
4.2-b12 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $135.8937927$ 2.826218305 \( -\frac{110887}{256} a^{2} + \frac{244753}{128} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 2 a^{3} - 10 a - 2\) , \( a^{3} - 5 a - 1\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}+\left(a^{3}+a^{2}-4a-3\right){y}={x}^{3}+\left(a^{3}-5a-1\right){x}^{2}+\left(2a^{3}-10a-2\right){x}+a^{3}-5a-1$
4.2-b13 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $543.5751710$ 2.826218305 \( \frac{110887}{256} a^{2} - \frac{64929}{256} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a\) , \( 0\) , \( 3\) , \( 1\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+3{x}+1$
4.2-b14 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $60.39724122$ 2.826218305 \( -\frac{55573026649}{16777216} a^{2} + \frac{25407190367}{16777216} \) \( \bigl[a^{3} + a^{2} - 4 a - 3\) , \( a^{3} - 5 a\) , \( 0\) , \( -10 a^{2} + 8\) , \( 20 a^{2} - 8\bigr] \) ${y}^2+\left(a^{3}+a^{2}-4a-3\right){x}{y}={x}^{3}+\left(a^{3}-5a\right){x}^{2}+\left(-10a^{2}+8\right){x}+20a^{2}-8$
4.2-b15 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.123340511$ 2.826218305 \( 179213540276326839556 a^{3} + 382760552527098253312 a^{2} - \frac{157151345464271319581}{2} a - 167820287562717580568 \) \( \bigl[a^{3} - 3 a + 1\) , \( 0\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 815 a^{3} + 529 a^{2} - 3702 a - 2452\) , \( 81105 a^{3} + 53660 a^{2} - 369901 a - 244920\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(815a^{3}+529a^{2}-3702a-2452\right){x}+81105a^{3}+53660a^{2}-369901a-244920$
4.2-b16 4.2-b 4.4.9248.1 \( 2^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.123340511$ 2.826218305 \( -179213540276326839556 a^{3} + 382760552527098253312 a^{2} + \frac{157151345464271319581}{2} a - 167820287562717580568 \) \( \bigl[a^{3} - 3 a + 1\) , \( -a^{3} + 3 a\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -816 a^{3} + 529 a^{2} + 3702 a - 2452\) , \( -81104 a^{3} + 53660 a^{2} + 369895 a - 244920\bigr] \) ${y}^2+\left(a^{3}-3a+1\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(-a^{3}+3a\right){x}^{2}+\left(-816a^{3}+529a^{2}+3702a-2452\right){x}-81104a^{3}+53660a^{2}+369895a-244920$
8.3-a1 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $644.2027085$ 1.674706263 \( -7659605 a^{2} + 34939686 \) \( \bigl[a^{2} - 2\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( 3 a^{2} - 17\) , \( -3 a^{2} + 12\bigr] \) ${y}^2+\left(a^{2}-2\right){x}{y}+\left(a^{2}-2\right){y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(3a^{2}-17\right){x}-3a^{2}+12$
8.3-a2 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $322.1013542$ 1.674706263 \( 343 a^{2} \) \( \bigl[a\) , \( a^{2} - 4\) , \( 0\) , \( 4\) , \( a^{2} - 2\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a^{2}-4\right){x}^{2}+4{x}+a^{2}-2$
8.3-a3 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1288.405417$ 1.674706263 \( 24225 a^{2} - 4222 \) \( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -a^{2} + 2\) , \( -a^{2}\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-a^{2}+2\right){x}-a^{2}$
8.3-a4 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $80.52533856$ 1.674706263 \( 2701312025 a^{2} - 1184382322 \) \( \bigl[a\) , \( a^{2} - 3\) , \( a\) , \( -11 a^{2} + 7\) , \( -36 a^{2} + 15\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(-11a^{2}+7\right){x}-36a^{2}+15$
8.3-a5 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $40.26266928$ 1.674706263 \( -1409277718922882 a^{3} - 933097728375808 a^{2} + 6428663656193677 a + 4256735329251048 \) \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 425 a^{3} + 317 a^{2} - 1940 a - 1450\) , \( 8542 a^{3} + 5847 a^{2} - 38964 a - 26670\bigr] \) ${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(425a^{3}+317a^{2}-1940a-1450\right){x}+8542a^{3}+5847a^{2}-38964a-26670$
8.3-a6 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $40.26266928$ 1.674706263 \( 1409277718922882 a^{3} - 933097728375808 a^{2} - 6428663656193677 a + 4256735329251048 \) \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( -425 a^{3} + 317 a^{2} + 1940 a - 1450\) , \( -8542 a^{3} + 5847 a^{2} + 38964 a - 26670\bigr] \) ${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(-425a^{3}+317a^{2}+1940a-1450\right){x}-8542a^{3}+5847a^{2}+38964a-26670$
8.3-a7 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $322.1013542$ 1.674706263 \( -21069823 a^{2} + 96961280 \) \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 37 a^{2} - 170\) , \( 181 a^{2} - 826\bigr] \) ${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(37a^{2}-170\right){x}+181a^{2}-826$
8.3-a8 8.3-a 4.4.9248.1 \( 2^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1288.405417$ 1.674706263 \( -1995 a^{2} + 11006 \) \( \bigl[a\) , \( 0\) , \( a^{3} - 4 a\) , \( 2 a^{2} - 10\) , \( 3 a^{2} - 14\bigr] \) ${y}^2+a{x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+\left(2a^{2}-10\right){x}+3a^{2}-14$
8.3-b1 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.246667540$ $4366.360965$ 1.399966817 \( 24225 a^{2} - 4222 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 4 a^{3} + 10 a^{2} - 7 a - 21\) , \( 9 a^{3} + 6 a^{2} - 21 a + 15\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(4a^{3}+10a^{2}-7a-21\right){x}+9a^{3}+6a^{2}-21a+15$
8.3-b2 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.123333770$ $1091.590241$ 1.399966817 \( 2701312025 a^{2} - 1184382322 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( 4 a^{3} - 7 a + 24\) , \( -a^{3} - 14 a^{2} + 24 a + 105\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}+a^{2}-4a-2\right){y}={x}^{3}+\left(a^{2}+a-2\right){x}^{2}+\left(4a^{3}-7a+24\right){x}-a^{3}-14a^{2}+24a+105$
8.3-b3 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.973340325$ $4.264024380$ 1.399966817 \( -1409277718922882 a^{3} - 933097728375808 a^{2} + 6428663656193677 a + 4256735329251048 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( -13 a^{3} - 41 a^{2} - 21 a - 2\) , \( -224 a^{3} - 527 a^{2} + 2 a + 165\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(-13a^{3}-41a^{2}-21a-2\right){x}-224a^{3}-527a^{2}+2a+165$
8.3-b4 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.986670162$ $68.22439009$ 1.399966817 \( -21069823 a^{2} + 96961280 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 2 a^{3} - a^{2} - a - 2\) , \( -3 a^{3} - 14 a^{2} + 3\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(2a^{3}-a^{2}-a-2\right){x}-3a^{3}-14a^{2}+3$
8.3-b5 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.493335081$ $1091.590241$ 1.399966817 \( -1995 a^{2} + 11006 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - a - 2\) , \( 2 a^{3} + 5 a^{2} - 3\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(2a^{3}+4a^{2}-a-2\right){x}+2a^{3}+5a^{2}-3$
8.3-b6 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.973340325$ $4.264024380$ 1.399966817 \( 1409277718922882 a^{3} - 933097728375808 a^{2} - 6428663656193677 a + 4256735329251048 \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a\) , \( a^{3} - 4 a\) , \( 17 a^{3} - 41 a^{2} + 19 a - 2\) , \( 138 a^{3} - 337 a^{2} - 2 a + 105\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}+a{x}^{2}+\left(17a^{3}-41a^{2}+19a-2\right){x}+138a^{3}-337a^{2}-2a+105$
8.3-b7 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.986670162$ $272.8975603$ 1.399966817 \( 343 a^{2} \) \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a + 1\) , \( a^{2} + a - 2\) , \( a^{3} + 3 a^{2} + 3 a + 3\) , \( 2 a^{3} + 7 a^{2} + 4 a - 4\bigr] \) ${y}^2+\left(a^{3}+a^{2}-3a-2\right){x}{y}+\left(a^{2}+a-2\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a^{3}+3a^{2}+3a+3\right){x}+2a^{3}+7a^{2}+4a-4$
8.3-b8 8.3-b 4.4.9248.1 \( 2^{3} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.123333770$ $2183.180482$ 1.399966817 \( -7659605 a^{2} + 34939686 \) \( \bigl[a^{3} - 4 a\) , \( -1\) , \( a^{3} - 4 a\) , \( -3\) , \( 6 a^{2} - 4\bigr] \) ${y}^2+\left(a^{3}-4a\right){x}{y}+\left(a^{3}-4a\right){y}={x}^{3}-{x}^{2}-3{x}+6a^{2}-4$
8.4-a1 8.4-a 4.4.9248.1 \( 2^{3} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.756986305$ $644.2027085$ 2.535459413 \( 7659605 a^{2} - 3358339 \) \( \bigl[a^{2} - 3\) , \( a^{2} - 2\) , \( a^{2} - 3\) , \( -3 a^{2} - 2\) , \( 3 a^{2} - 3\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}-3\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{2}-2\right){x}+3a^{2}-3$
8.4-a2 8.4-a 4.4.9248.1 \( 2^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.378493152$ $322.1013542$ 2.535459413 \( -343 a^{2} + 1715 \) \( \bigl[a + 1\) , \( -a^{3} + a^{2} + 5 a - 4\) , \( a^{3} - 4 a + 1\) , \( 3 a^{3} - 10 a + 8\) , \( -5 a^{3} - 4 a^{2} + 12 a - 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a^{3}-4a+1\right){y}={x}^{3}+\left(-a^{3}+a^{2}+5a-4\right){x}^{2}+\left(3a^{3}-10a+8\right){x}-5a^{3}-4a^{2}+12a-5$
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  *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.