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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
1.1-a1 1.1-a \(\Q(\sqrt{301}) \) \( 1 \) 0 $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.377014941 \( -3375 \) \( \bigl[a\) , \( -a\) , \( a\) , \( 400 a - 3665\) , \( -12979 a + 119119\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(400a-3665\right){x}-12979a+119119$
1.1-a2 1.1-a \(\Q(\sqrt{301}) \) \( 1 \) 0 $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.377014941 \( -3375 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -402 a - 3265\) , \( 12978 a + 106140\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-402a-3265\right){x}+12978a+106140$
1.1-a3 1.1-a \(\Q(\sqrt{301}) \) \( 1 \) 0 $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.377014941 \( 16581375 \) \( \bigl[a\) , \( -a\) , \( a\) , \( 6955 a - 63805\) , \( -874060 a + 8019258\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(6955a-63805\right){x}-874060a+8019258$
1.1-a4 1.1-a \(\Q(\sqrt{301}) \) \( 1 \) 0 $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $1$ $26.16385905$ 0.377014941 \( 16581375 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -6957 a - 56850\) , \( 874059 a + 7145198\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-6957a-56850\right){x}+874059a+7145198$
3.1-a1 3.1-a \(\Q(\sqrt{301}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.554611758$ $20.97578440$ 4.023233935 \( \frac{5404}{27} a + \frac{22925}{27} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -76 a - 398\) , \( 200 a + 2277\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-76a-398\right){x}+200a+2277$
3.1-b1 3.1-b \(\Q(\sqrt{301}) \) \( 3 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.221630154$ $40.46933302$ 2.067910033 \( \frac{5404}{27} a + \frac{22925}{27} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 4331 a - 39735\) , \( -815041 a + 7477737\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(4331a-39735\right){x}-815041a+7477737$
3.2-a1 3.2-a \(\Q(\sqrt{301}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.554611758$ $20.97578440$ 4.023233935 \( -\frac{5404}{27} a + \frac{9443}{9} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 76 a - 474\) , \( -200 a + 2477\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(76a-474\right){x}-200a+2477$
3.2-b1 3.2-b \(\Q(\sqrt{301}) \) \( 3 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.221630154$ $40.46933302$ 2.067910033 \( -\frac{5404}{27} a + \frac{9443}{9} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -4331 a - 35404\) , \( 815041 a + 6662696\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+\left(-4331a-35404\right){x}+815041a+6662696$
9.2-a1 9.2-a \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.152714218$ $10.13145612$ 5.385180412 \( \frac{5404}{27} a + \frac{22925}{27} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 1277529 a - 11720610\) , \( 4141777236 a - 37999462298\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(1277529a-11720610\right){x}+4141777236a-37999462298$
9.2-b1 9.2-b \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.870390261$ $27.92872660$ 5.604564885 \( \frac{5404}{27} a + \frac{22925}{27} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 20 a + 168\) , \( 64 a + 525\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(20a+168\right){x}+64a+525$
9.2-c1 9.2-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $2.358552390$ $39.96595486$ 5.433159735 \( -3375 \) \( \bigl[1\) , \( -1\) , \( a\) , \( -13 a - 102\) , \( 90 a + 719\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-13a-102\right){x}+90a+719$
9.2-c2 9.2-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $16.50986673$ $5.709422123$ 5.433159735 \( -3375 \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 120854 a - 1108595\) , \( 83293389 a - 764189269\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(120854a-1108595\right){x}+83293389a-764189269$
9.2-c3 9.2-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $1.179276195$ $39.96595486$ 5.433159735 \( 16581375 \) \( \bigl[1\) , \( -1\) , \( a\) , \( -213 a - 1737\) , \( 5019 a + 41012\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-213a-1737\right){x}+5019a+41012$
9.2-c4 9.2-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $8.254933368$ $5.709422123$ 5.433159735 \( 16581375 \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 2054379 a - 18848060\) , \( 4728597369 a - 43383347215\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(2054379a-18848060\right){x}+4728597369a-43383347215$
9.3-a1 9.3-a \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.152714218$ $10.13145612$ 5.385180412 \( -\frac{5404}{27} a + \frac{9443}{9} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -1277489 a - 10443044\) , \( -4153497845 a - 33953498256\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1277489a-10443044\right){x}-4153497845a-33953498256$
9.3-b1 9.3-b \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.870390261$ $27.92872660$ 5.604564885 \( -\frac{5404}{27} a + \frac{9443}{9} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 18 a + 113\) , \( 66 a + 495\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(18a+113\right){x}+66a+495$
9.3-c1 9.3-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $16.50986673$ $5.709422123$ 5.433159735 \( -3375 \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -120855 a - 987740\) , \( -83293389 a - 680895880\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-120855a-987740\right){x}-83293389a-680895880$
9.3-c2 9.3-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-7$ $N(\mathrm{U}(1))$ $2.358552390$ $39.96595486$ 5.433159735 \( -3375 \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 12 a - 115\) , \( -91 a + 809\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(12a-115\right){x}-91a+809$
9.3-c3 9.3-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $8.254933368$ $5.709422123$ 5.433159735 \( 16581375 \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -2054380 a - 16793680\) , \( -4728597369 a - 38654749846\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-2054380a-16793680\right){x}-4728597369a-38654749846$
9.3-c4 9.3-c \(\Q(\sqrt{301}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $-28$ $N(\mathrm{U}(1))$ $1.179276195$ $39.96595486$ 5.433159735 \( 16581375 \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 212 a - 1950\) , \( -5020 a + 46031\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(212a-1950\right){x}-5020a+46031$
15.1-a1 15.1-a \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.93354958$ 4.365246621 \( -\frac{403177472}{18225} a - \frac{3273392128}{18225} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -1910572 a + 17528879\) , \( 2687078497 a - 24653074023\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(-1910572a+17528879\right){x}+2687078497a-24653074023$
15.1-a2 15.1-a \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.93354958$ 4.365246621 \( \frac{24051712}{140625} a - \frac{169050112}{140625} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 90938 a + 743389\) , \( 84627209 a + 691799996\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(90938a+743389\right){x}+84627209a+691799996$
15.1-b1 15.1-b \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.384850921$ 3.724531766 \( -\frac{403177472}{18225} a - \frac{3273392128}{18225} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -8 a - 65\) , \( -39 a - 319\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(-8a-65\right){x}-39a-319$
15.1-b2 15.1-b \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.384850921$ 3.724531766 \( \frac{24051712}{140625} a - \frac{169050112}{140625} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 42 a - 385\) , \( 577 a - 5294\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(42a-385\right){x}+577a-5294$
15.2-a1 15.2-a \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.742329761$ $6.799969143$ 5.237126591 \( \frac{3565416510442094}{52734375} a - \frac{10903846831184923}{17578125} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 249169 a - 2286010\) , \( -197430230 a + 1811358398\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(249169a-2286010\right){x}-197430230a+1811358398$
15.2-b1 15.2-b \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $54.53642909$ 3.143427514 \( -\frac{3368038}{15} a - \frac{9182149}{5} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 16 a + 106\) , \( 45 a + 353\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(16a+106\right){x}+45a+353$
15.2-c1 15.2-c \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.829291155$ 0.278355714 \( -\frac{3368038}{15} a - \frac{9182149}{5} \) \( \bigl[a\) , \( a\) , \( a\) , \( 561064 a - 5147318\) , \( 1143855488 a - 10494502248\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(561064a-5147318\right){x}+1143855488a-10494502248$
15.2-d1 15.2-d \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.476069346$ $1.723394042$ 1.475758840 \( \frac{3565416510442094}{52734375} a - \frac{10903846831184923}{17578125} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 1026 a + 8446\) , \( 2723356 a + 22262631\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(1026a+8446\right){x}+2723356a+22262631$
15.3-a1 15.3-a \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.742329761$ $6.799969143$ 5.237126591 \( -\frac{3565416510442094}{52734375} a - \frac{1165844959324507}{2109375} \) \( \bigl[a + 1\) , \( 1\) , \( a\) , \( -249169 a - 2036841\) , \( 197181061 a + 1611891327\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-249169a-2036841\right){x}+197181061a+1611891327$
15.3-b1 15.3-b \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $54.53642909$ 3.143427514 \( \frac{3368038}{15} a - \frac{6182897}{3} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 22 a + 123\) , \( 61 a + 567\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22a+123\right){x}+61a+567$
15.3-c1 15.3-c \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.829291155$ 0.278355714 \( \frac{3368038}{15} a - \frac{6182897}{3} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( -561025 a - 4586216\) , \( -1149002768 a - 9392725116\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-561025a-4586216\right){x}-1149002768a-9392725116$
15.3-d1 15.3-d \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.476069346$ $1.723394042$ 1.475758840 \( -\frac{3565416510442094}{52734375} a - \frac{1165844959324507}{2109375} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -1027 a + 9473\) , \( -2723356 a + 24985987\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1027a+9473\right){x}-2723356a+24985987$
15.4-a1 15.4-a \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.93354958$ 4.365246621 \( -\frac{24051712}{140625} a - \frac{1933312}{1875} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( -90938 a + 834327\) , \( -84627209 a + 776427205\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(-90938a+834327\right){x}-84627209a+776427205$
15.4-a2 15.4-a \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $18.93354958$ 4.365246621 \( \frac{403177472}{18225} a - \frac{49020928}{243} \) \( \bigl[0\) , \( -1\) , \( 1\) , \( 1910572 a + 15618307\) , \( -2687078497 a - 21965995526\bigr] \) ${y}^2+{y}={x}^{3}-{x}^{2}+\left(1910572a+15618307\right){x}-2687078497a-21965995526$
15.4-b1 15.4-b \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.384850921$ 3.724531766 \( -\frac{24051712}{140625} a - \frac{1933312}{1875} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -42 a - 343\) , \( -577 a - 4717\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(-42a-343\right){x}-577a-4717$
15.4-b2 15.4-b \(\Q(\sqrt{301}) \) \( 3 \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.384850921$ 3.724531766 \( \frac{403177472}{18225} a - \frac{49020928}{243} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 8 a - 73\) , \( 39 a - 358\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+\left(8a-73\right){x}+39a-358$
20.1-a1 20.1-a \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $22.28759743$ 5.138543038 \( -\frac{102081}{20} a + \frac{1870817}{40} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 11440 a - 104961\) , \( 2035889 a - 18678595\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(11440a-104961\right){x}+2035889a-18678595$
20.1-a2 20.1-a \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $22.28759743$ 5.138543038 \( -\frac{486003}{250} a + \frac{2236489}{125} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4082737 a + 33375119\) , \( -72075964995 a - 589197645731\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(4082737a+33375119\right){x}-72075964995a-589197645731$
20.1-b1 20.1-b \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $0 \le r \le 1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.049999803$ 6.703766758 \( -\frac{5031337703}{40} a - \frac{41129472787}{40} \) \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -20678976 a - 169043910\) , \( -151007863785 a - 1234440327640\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-20678976a-169043910\right){x}-151007863785a-1234440327640$
20.1-c1 20.1-c \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.552386710$ $31.00673775$ 3.948899142 \( -\frac{5031337703}{40} a - \frac{41129472787}{40} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 20 a + 94\) , \( 80 a + 360\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a+94\right){x}+80a+360$
20.1-d1 20.1-d \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.734562548$ $20.58488197$ 1.743106455 \( -\frac{102081}{20} a + \frac{1870817}{40} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -68 a - 530\) , \( -6625 a - 54095\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-68a-530\right){x}-6625a-54095$
20.1-d2 20.1-d \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.244854182$ $20.58488197$ 1.743106455 \( -\frac{486003}{250} a + \frac{2236489}{125} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -10 a + 105\) , \( -31 a + 343\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+105\right){x}-31a+343$
20.2-a1 20.2-a \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $22.28759743$ 5.138543038 \( \frac{486003}{250} a + \frac{159479}{10} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -4082737 a + 37457781\) , \( 72080047731 a - 661311068582\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4082737a+37457781\right){x}+72080047731a-661311068582$
20.2-a2 20.2-a \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $22.28759743$ 5.138543038 \( \frac{102081}{20} a + \frac{333331}{8} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -11439 a - 93446\) , \( -2047329 a - 16736152\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-11439a-93446\right){x}-2047329a-16736152$
20.2-b1 20.2-b \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $0 \le r \le 1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.049999803$ 6.703766758 \( \frac{5031337703}{40} a - \frac{4616081049}{4} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 20679016 a - 189722963\) , \( 150818140823 a - 1383707543744\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(20679016a-189722963\right){x}+150818140823a-1383707543744$
20.2-c1 20.2-c \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.552386710$ $31.00673775$ 3.948899142 \( \frac{5031337703}{40} a - \frac{4616081049}{4} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 18 a + 151\) , \( 33 a + 271\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(18a+151\right){x}+33a+271$
20.2-d1 20.2-d \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.244854182$ $20.58488197$ 1.743106455 \( \frac{486003}{250} a + \frac{159479}{10} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 8 a + 95\) , \( 30 a + 312\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(8a+95\right){x}+30a+312$
20.2-d2 20.2-d \(\Q(\sqrt{301}) \) \( 2^{2} \cdot 5 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.734562548$ $20.58488197$ 1.743106455 \( \frac{102081}{20} a + \frac{333331}{8} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 66 a - 597\) , \( 6624 a - 60720\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(66a-597\right){x}+6624a-60720$
25.1-a1 25.1-a \(\Q(\sqrt{301}) \) \( 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.199506422$ $12.17791294$ 5.051768556 \( -\frac{110592}{125} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( -1311 a - 10717\) , \( -130778 a - 1069068\bigr] \) ${y}^2+{y}={x}^{3}+\left(-1311a-10717\right){x}-130778a-1069068$
25.1-b1 25.1-b \(\Q(\sqrt{301}) \) \( 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.199506422$ $12.17791294$ 5.051768556 \( -\frac{110592}{125} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 1311 a - 12028\) , \( 130778 a - 1199846\bigr] \) ${y}^2+{y}={x}^{3}+\left(1311a-12028\right){x}+130778a-1199846$
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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.