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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
8.1-a1 8.1-a \(\Q(\sqrt{23}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.290517010$ $17.55912210$ 2.127357326 \( 256 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -80 a + 384\) , \( 2072 a - 9937\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-80a+384\right){x}+2072a-9937$
8.1-b1 8.1-b \(\Q(\sqrt{23}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.290517010$ $17.55912210$ 2.127357326 \( 256 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -80 a + 384\) , \( -2072 a + 9937\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-80a+384\right){x}-2072a+9937$
9.1-a1 9.1-a \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.671003177$ $11.01298155$ 1.533399817 \( -\frac{2924207}{81} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 715 a - 3429\) , \( -23270 a + 111599\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(715a-3429\right){x}-23270a+111599$
9.1-a2 9.1-a \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $10.68401271$ $11.01298155$ 1.533399817 \( -\frac{576110079740793605}{3} a + 920975627106405096 \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -11590 a - 55573\) , \( -1475005 a - 7073869\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-11590a-55573\right){x}-1475005a-7073869$
9.1-a3 9.1-a \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $5.342006355$ $11.01298155$ 1.533399817 \( \frac{12214672127}{9} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 11515 a - 55224\) , \( -1472000 a + 7059464\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(11515a-55224\right){x}-1472000a+7059464$
9.1-a4 9.1-a \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $10.68401271$ $2.753245389$ 1.533399817 \( \frac{576110079740793605}{3} a + 920975627106405096 \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 11590 a - 55584\) , \( -1451825 a + 6962708\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(11590a-55584\right){x}-1451825a+6962708$
9.1-b1 9.1-b \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.671003177$ $11.01298155$ 1.533399817 \( -\frac{2924207}{81} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 715 a - 3418\) , \( 24700 a - 118450\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(715a-3418\right){x}+24700a-118450$
9.1-b2 9.1-b \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $10.68401271$ $2.753245389$ 1.533399817 \( -\frac{576110079740793605}{3} a + 920975627106405096 \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -11590 a - 55584\) , \( 1451825 a + 6962708\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-11590a-55584\right){x}+1451825a+6962708$
9.1-b3 9.1-b \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $5.342006355$ $11.01298155$ 1.533399817 \( \frac{12214672127}{9} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 11515 a - 55213\) , \( 1495030 a - 7169905\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(11515a-55213\right){x}+1495030a-7169905$
9.1-b4 9.1-b \(\Q(\sqrt{23}) \) \( 3^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $10.68401271$ $11.01298155$ 1.533399817 \( \frac{576110079740793605}{3} a + 920975627106405096 \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 11590 a - 55573\) , \( 1475005 a - 7073869\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(11590a-55573\right){x}+1475005a-7073869$
11.1-a1 11.1-a \(\Q(\sqrt{23}) \) \( 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $13.63633641$ 1.421686348 \( \frac{8066560}{1331} a + \frac{40525632}{1331} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 6 a + 24\) , \( 11 a + 45\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(6a+24\right){x}+11a+45$
11.1-b1 11.1-b \(\Q(\sqrt{23}) \) \( 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.114283851$ $26.97262573$ 1.928259279 \( \frac{8066560}{1331} a + \frac{40525632}{1331} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 4 a + 16\) , \( 7 a + 26\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+16\right){x}+7a+26$
11.2-a1 11.2-a \(\Q(\sqrt{23}) \) \( 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $13.63633641$ 1.421686348 \( -\frac{8066560}{1331} a + \frac{40525632}{1331} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 7 a + 35\) , \( 13 a + 62\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(7a+35\right){x}+13a+62$
11.2-b1 11.2-b \(\Q(\sqrt{23}) \) \( 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.114283851$ $26.97262573$ 1.928259279 \( -\frac{8066560}{1331} a + \frac{40525632}{1331} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 5 a + 27\) , \( 9 a + 43\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+27\right){x}+9a+43$
16.1-a1 16.1-a \(\Q(\sqrt{23}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.463514535$ $25.95485587$ 2.508522851 \( -12800 a - 60672 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11\) , \( -a - 2\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+11{x}-a-2$
16.1-b1 16.1-b \(\Q(\sqrt{23}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.547762297$ $8.850540007$ 2.856341401 \( 12800 a - 60672 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 11\) , \( -a + 2\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+11{x}-a+2$
16.1-c1 16.1-c \(\Q(\sqrt{23}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.463514535$ $25.95485587$ 2.508522851 \( 12800 a - 60672 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 11\) , \( a - 2\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+11{x}+a-2$
16.1-d1 16.1-d \(\Q(\sqrt{23}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.547762297$ $8.850540007$ 2.856341401 \( -12800 a - 60672 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 11\) , \( a + 2\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+11{x}+a+2$
22.1-a1 22.1-a \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.546132399$ 0.530905305 \( \frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 272 a - 1296\) , \( 5885 a - 28217\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(272a-1296\right){x}+5885a-28217$
22.1-a2 22.1-a \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $22.91519159$ 0.530905305 \( \frac{723699}{22} a + \frac{1731269}{11} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 2 a - 1\) , \( 16 a - 70\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(2a-1\right){x}+16a-70$
22.1-b1 22.1-b \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.065464909$ $24.74161214$ 2.026394031 \( \frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 272 a - 1307\) , \( -5340 a + 25604\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(272a-1307\right){x}-5340a+25604$
22.1-b2 22.1-b \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.196394727$ $24.74161214$ 2.026394031 \( \frac{723699}{22} a + \frac{1731269}{11} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 2 a - 12\) , \( -11 a + 47\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(2a-12\right){x}-11a+47$
22.2-a1 22.2-a \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.546132399$ 0.530905305 \( -\frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( -273 a - 1296\) , \( -5885 a - 28217\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-273a-1296\right){x}-5885a-28217$
22.2-a2 22.2-a \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $22.91519159$ 0.530905305 \( -\frac{723699}{22} a + \frac{1731269}{11} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( -3 a - 1\) , \( -16 a - 70\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-3a-1\right){x}-16a-70$
22.2-b1 22.2-b \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.065464909$ $24.74161214$ 2.026394031 \( -\frac{888928020465}{10648} a - \frac{2131508856307}{5324} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -273 a - 1307\) , \( 5340 a + 25604\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-273a-1307\right){x}+5340a+25604$
22.2-b2 22.2-b \(\Q(\sqrt{23}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.196394727$ $24.74161214$ 2.026394031 \( -\frac{723699}{22} a + \frac{1731269}{11} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -3 a - 12\) , \( 11 a + 47\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-3a-12\right){x}+11a+47$
25.1-a1 25.1-a \(\Q(\sqrt{23}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $12.39496478$ 1.292264409 \( -\frac{32768}{125} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -160 a - 767\) , \( -6594 a - 31624\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(-160a-767\right){x}-6594a-31624$
25.1-b1 25.1-b \(\Q(\sqrt{23}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $12.39496478$ 1.292264409 \( -\frac{32768}{125} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -160 a - 767\) , \( 6594 a + 31618\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-160a-767\right){x}+6594a+31618$
26.1-a1 26.1-a \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.25262699$ 3.805935822 \( \frac{74750337}{169} a - \frac{1433958043}{676} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( a + 12\) , \( -31 a - 150\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+12\right){x}-31a-150$
26.1-a2 26.1-a \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.25262699$ 3.805935822 \( -\frac{24402922831899}{13} a + \frac{234064614018301}{26} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -59 a - 278\) , \( -421 a - 2022\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-59a-278\right){x}-421a-2022$
26.1-b1 26.1-b \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.101360370$ $22.55344511$ 4.290023491 \( \frac{1169733145}{70304} a - \frac{5737718647}{70304} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 25 a - 109\) , \( -102 a + 496\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(25a-109\right){x}-102a+496$
26.1-c1 26.1-c \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.968415518$ $2.373126329$ 4.312818575 \( \frac{1169733145}{70304} a - \frac{5737718647}{70304} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 25 a - 120\) , \( 152 a - 729\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(25a-120\right){x}+152a-729$
26.1-d1 26.1-d \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.211018668$ 1.295086918 \( \frac{74750337}{169} a - \frac{1433958043}{676} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 5 a + 16\) , \( 37 a + 174\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+16\right){x}+37a+174$
26.1-d2 26.1-d \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.211018668$ 1.295086918 \( -\frac{24402922831899}{13} a + \frac{234064614018301}{26} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -55 a - 274\) , \( 307 a + 1466\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-55a-274\right){x}+307a+1466$
26.2-a1 26.2-a \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.25262699$ 3.805935822 \( -\frac{74750337}{169} a - \frac{1433958043}{676} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 12\) , \( 30 a - 150\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-2a+12\right){x}+30a-150$
26.2-a2 26.2-a \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.25262699$ 3.805935822 \( \frac{24402922831899}{13} a + \frac{234064614018301}{26} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 58 a - 278\) , \( 420 a - 2022\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(58a-278\right){x}+420a-2022$
26.2-b1 26.2-b \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.101360370$ $22.55344511$ 4.290023491 \( -\frac{1169733145}{70304} a - \frac{5737718647}{70304} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -25 a - 109\) , \( 102 a + 496\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-25a-109\right){x}+102a+496$
26.2-c1 26.2-c \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.968415518$ $2.373126329$ 4.312818575 \( -\frac{1169733145}{70304} a - \frac{5737718647}{70304} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -25 a - 120\) , \( -152 a - 729\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-25a-120\right){x}-152a-729$
26.2-d1 26.2-d \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.211018668$ 1.295086918 \( -\frac{74750337}{169} a - \frac{1433958043}{676} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -6 a + 16\) , \( -38 a + 174\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+16\right){x}-38a+174$
26.2-d2 26.2-d \(\Q(\sqrt{23}) \) \( 2 \cdot 13 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.211018668$ 1.295086918 \( \frac{24402922831899}{13} a + \frac{234064614018301}{26} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 54 a - 274\) , \( -308 a + 1466\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(54a-274\right){x}-308a+1466$
28.1-a1 28.1-a \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $29.39740986$ 2.298668884 \( \frac{1472}{7} a + \frac{8464}{7} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 5 a + 24\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(5a+24\right){x}$
28.1-a2 28.1-a \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $14.69870493$ 2.298668884 \( \frac{8732868}{49} a + \frac{42307568}{49} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -20 a - 96\) , \( -284 a - 1362\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-20a-96\right){x}-284a-1362$
28.1-b1 28.1-b \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.760351911$ $23.50334847$ 2.794742034 \( \frac{1472}{7} a + \frac{8464}{7} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2 a + 4\) , \( -4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+4\right){x}-4$
28.1-b2 28.1-b \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.380175955$ $23.50334847$ 2.794742034 \( \frac{8732868}{49} a + \frac{42307568}{49} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -23 a - 116\) , \( 64 a + 303\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-23a-116\right){x}+64a+303$
28.2-a1 28.2-a \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $29.39740986$ 2.298668884 \( -\frac{1472}{7} a + \frac{8464}{7} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 8 a + 12\) , \( 12 a + 40\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+12\right){x}+12a+40$
28.2-a2 28.2-a \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $14.69870493$ 2.298668884 \( -\frac{8732868}{49} a + \frac{42307568}{49} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 33 a - 108\) , \( 176 a - 747\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-108\right){x}+176a-747$
28.2-b1 28.2-b \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.760351911$ $23.50334847$ 2.794742034 \( -\frac{1472}{7} a + \frac{8464}{7} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 7 a + 16\) , \( 4 a + 48\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+16\right){x}+4a+48$
28.2-b2 28.2-b \(\Q(\sqrt{23}) \) \( 2^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.380175955$ $23.50334847$ 2.794742034 \( -\frac{8732868}{49} a + \frac{42307568}{49} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 32 a - 104\) , \( -180 a + 930\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(32a-104\right){x}-180a+930$
46.1-a1 46.1-a \(\Q(\sqrt{23}) \) \( 2 \cdot 23 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.101081815$ $1.747176977$ 1.494071611 \( -\frac{116930169}{23552} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -10\) , \( -12\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-10{x}-12$
46.1-a2 46.1-a \(\Q(\sqrt{23}) \) \( 2 \cdot 23 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.050540907$ $1.747176977$ 1.494071611 \( \frac{545138290809}{16928} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -170\) , \( -812\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-170{x}-812$
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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.