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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
450.3-a1 450.3-a \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $22.94110692$ 7.254614994 \( -\frac{5929}{6} a - \frac{3925}{3} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( a - 8\) , \( 2 a - 3\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(a-8\right){x}+2a-3$
450.3-b1 450.3-b \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.284580539$ 4.062200343 \( -\frac{259064095}{1944} a - \frac{318409405}{972} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1781 a - 5733\) , \( -69214 a + 218498\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1781a-5733\right){x}-69214a+218498$
450.3-b2 450.3-b \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $6.422902698$ 4.062200343 \( -\frac{29499775}{6} a + \frac{46646975}{3} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 161 a - 513\) , \( 2378 a - 7522\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(161a-513\right){x}+2378a-7522$
450.3-c1 450.3-c \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.459097436$ 7.113788473 \( -\frac{574055084970269951}{6} a - \frac{907661070264560078}{3} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -60681 a - 193668\) , \( 14402517 a + 45516541\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-60681a-193668\right){x}+14402517a+45516541$
450.3-c2 450.3-c \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.213682052$ 7.113788473 \( -\frac{7261339}{34992} a + \frac{5642407}{8748} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -6 a - 18\) , \( 267 a + 841\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6a-18\right){x}+267a+841$
450.3-d1 450.3-d \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.498297114$ 2.371169745 \( -\frac{546421}{50} a - \frac{161087}{40} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 5 a - 100\) , \( 100 a - 125\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(5a-100\right){x}+100a-125$
450.3-d2 450.3-d \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.498297114$ 2.371169745 \( -\frac{77254}{5} a + \frac{100565}{2} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 111 a - 357\) , \( -1013 a + 3201\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(111a-357\right){x}-1013a+3201$
450.3-d3 450.3-d \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.498297114$ 2.371169745 \( -\frac{15308292191}{10} a + \frac{24204545642}{5} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 1786 a - 5657\) , \( -71168 a + 225051\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(1786a-5657\right){x}-71168a+225051$
450.3-d4 450.3-d \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.498297114$ 2.371169745 \( \frac{122257133981}{500} a + \frac{96653122463}{125} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -195 a - 900\) , \( 2980 a + 10675\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-195a-900\right){x}+2980a+10675$
450.3-e1 450.3-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.494232175$ $3.362932028$ 4.204739475 \( -\frac{738259}{750} a + \frac{938257}{300} \) \( \bigl[a\) , \( a\) , \( a\) , \( 30 a - 65\) , \( -175 a + 110\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(30a-65\right){x}-175a+110$
450.3-e2 450.3-e \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.988464351$ $1.681466014$ 4.204739475 \( \frac{210156181}{56250} a + \frac{684296471}{56250} \) \( \bigl[a\) , \( a\) , \( a\) , \( -170 a - 265\) , \( -2135 a - 3290\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-170a-265\right){x}-2135a-3290$
450.3-f1 450.3-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $8.736672867$ 1.841852362 \( -\frac{533474309}{12} a + \frac{843496315}{6} \) \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( 10 a - 56\) , \( -13 a + 248\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(10a-56\right){x}-13a+248$
450.3-f2 450.3-f \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.912224289$ 1.841852362 \( -\frac{225727}{864} a + \frac{400355}{432} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 351 a + 1117\) , \( -25774 a - 81502\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(351a+1117\right){x}-25774a-81502$
450.3-g1 450.3-g \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $8.044960389$ $0.424816695$ 4.323002413 \( -\frac{23469020634623}{1259712} a - \frac{18555184937575}{314928} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 10 a - 182\) , \( 158 a - 1174\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(10a-182\right){x}+158a-1174$
450.3-g2 450.3-g \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $24.13488116$ $0.141605565$ 4.323002413 \( \frac{62509658925710141}{3538944} a - \frac{49418224549259105}{884736} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2870 a - 9157\) , \( 152827 a - 484589\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2870a-9157\right){x}+152827a-484589$
450.3-h1 450.3-h \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.868067703$ 1.223190408 \( -\frac{172364765}{2} a + 272489285 \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -198 a - 636\) , \( 2489 a + 7858\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-198a-636\right){x}+2489a+7858$
450.3-h2 450.3-h \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.868067703$ 1.223190408 \( -\frac{295}{4} a + \frac{3205}{2} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 31 a + 17\) , \( 86 a - 2\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(31a+17\right){x}+86a-2$
450.3-i1 450.3-i \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.477384821$ $3.258409817$ 6.886560190 \( \frac{1099493}{16} a - \frac{462131}{2} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1006 a - 3188\) , \( -28864 a + 91268\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1006a-3188\right){x}-28864a+91268$
450.3-i2 450.3-i \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.159128273$ $3.258409817$ 6.886560190 \( \frac{454513}{2048} a + \frac{260987}{256} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 22\) , \( -15 a + 31\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+22{x}-15a+31$
450.3-j1 450.3-j \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.467034057$ 4.175252124 \( -\frac{172364765}{2} a + 272489285 \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 128 a - 403\) , \( 1447 a - 4583\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(128a-403\right){x}+1447a-4583$
450.3-j2 450.3-j \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $13.20330651$ 4.175252124 \( -\frac{295}{4} a + \frac{3205}{2} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 3 a - 3\) , \( 2 a - 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(3a-3\right){x}+2a-3$
450.3-k1 450.3-k \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.602619814$ 1.139248415 \( -\frac{97959672159615035}{12} a - \frac{154887841432390445}{6} \) \( \bigl[a\) , \( a\) , \( a\) , \( -340 a - 6105\) , \( 56355 a + 42690\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-340a-6105\right){x}+56355a+42690$
450.3-k2 450.3-k \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.200873271$ 1.139248415 \( -\frac{130644467741576305}{54} a + \frac{206567040871853915}{27} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -532 a - 2251\) , \( 15096 a + 43018\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-532a-2251\right){x}+15096a+43018$
450.3-k3 450.3-k \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.602619814$ 1.139248415 \( -\frac{78338627675}{62208} a + \frac{123816286975}{31104} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 314 a - 1057\) , \( -5258 a + 16911\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(314a-1057\right){x}-5258a+16911$
450.3-k4 450.3-k \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.200873271$ 1.139248415 \( -\frac{30057855025}{114791256} a + \frac{101192416175}{57395628} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 735 a + 2220\) , \( -15720 a - 49925\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(735a+2220\right){x}-15720a-49925$
450.3-l1 450.3-l \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.683879708$ $2.440475417$ 2.599055159 \( -\frac{7361303}{4860} a + \frac{9044707}{3888} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 260 a - 843\) , \( -3460 a + 10897\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(260a-843\right){x}-3460a+10897$
450.3-l2 450.3-l \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.683879708$ $0.610118854$ 2.599055159 \( \frac{20775046733269}{34867844010} a + \frac{361175517267013}{174339220050} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -1540 a + 4557\) , \( 158740 a - 503703\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-1540a+4557\right){x}+158740a-503703$
450.3-l3 450.3-l \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.367759416$ $1.220237708$ 2.599055159 \( \frac{184784183669}{118098} a + \frac{5854047089047}{1180980} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 1060 a - 3643\) , \( 32220 a - 103903\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1060a-3643\right){x}+32220a-103903$
450.3-l4 450.3-l \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.735518833$ $0.305059427$ 2.599055159 \( \frac{37688339331809089}{2430} a + \frac{23836231835693689}{486} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 16460 a - 56643\) , \( 2170020 a - 6984103\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(16460a-56643\right){x}+2170020a-6984103$
450.3-m1 450.3-m \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.485977887$ $3.602619814$ 6.771591819 \( -\frac{97959672159615035}{12} a - \frac{154887841432390445}{6} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -85 a - 1528\) , \( 7002 a + 4572\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-85a-1528\right){x}+7002a+4572$
450.3-m2 450.3-m \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $4.457933663$ $1.200873271$ 6.771591819 \( -\frac{130644467741576305}{54} a + \frac{206567040871853915}{27} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2129 a - 9013\) , \( 127656 a + 356418\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2129a-9013\right){x}+127656a+356418$
450.3-m3 450.3-m \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.297195577$ $3.602619814$ 6.771591819 \( -\frac{78338627675}{62208} a + \frac{123816286975}{31104} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1256 a - 4228\) , \( -42064 a + 135288\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1256a-4228\right){x}-42064a+135288$
450.3-m4 450.3-m \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.891586732$ $1.200873271$ 6.771591819 \( -\frac{30057855025}{114791256} a + \frac{101192416175}{57395628} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 182 a + 557\) , \( -2243 a - 7159\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(182a+557\right){x}-2243a-7159$
450.3-n1 450.3-n \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.578502414$ 1.497498876 \( \frac{1181545}{108} a - \frac{1128415}{27} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -2 a - 11\) , \( -9 a - 32\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-2a-11\right){x}-9a-32$
450.3-n2 450.3-n \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $4.735507243$ 1.497498876 \( \frac{8885}{96} a + \frac{33055}{24} \) \( \bigl[a\) , \( a\) , \( a\) , \( -40 a + 135\) , \( 215 a - 670\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-40a+135\right){x}+215a-670$
450.3-o1 450.3-o \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.977110452$ $3.677182728$ 2.272421378 \( -\frac{349938025}{8} \) \( \bigl[a\) , \( a\) , \( a\) , \( -400 a - 1305\) , \( 7199 a + 22690\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-400a-1305\right){x}+7199a+22690$
450.3-o2 450.3-o \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.628517420$ $2.206309637$ 2.272421378 \( -\frac{121945}{32} \) \( \bigl[a\) , \( a\) , \( a\) , \( -240 a - 785\) , \( -4945 a - 15590\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-240a-785\right){x}-4945a-15590$
450.3-o3 450.3-o \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.325703484$ $11.03154818$ 2.272421378 \( -\frac{25}{2} \) \( \bigl[a\) , \( a\) , \( a\) , \( -5\) , \( 23 a + 70\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}-5{x}+23a+70$
450.3-o4 450.3-o \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $4.885552262$ $0.735436545$ 2.272421378 \( \frac{46969655}{32768} \) \( \bigl[a\) , \( a\) , \( a\) , \( 1760 a + 5715\) , \( 36455 a + 114910\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(1760a+5715\right){x}+36455a+114910$
450.3-p1 450.3-p \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $3.677182728$ 3.488481838 \( -\frac{349938025}{8} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -100 a - 328\) , \( 850 a + 2672\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-100a-328\right){x}+850a+2672$
450.3-p2 450.3-p \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.206309637$ 3.488481838 \( -\frac{121945}{32} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -60 a - 198\) , \( -648 a - 2048\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-60a-198\right){x}-648a-2048$
450.3-p3 450.3-p \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $11.03154818$ 3.488481838 \( -\frac{25}{2} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -3\) , \( 3 a + 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}-3{x}+3a+7$
450.3-p4 450.3-p \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.735436545$ 3.488481838 \( \frac{46969655}{32768} \) \( \bigl[a + 1\) , \( 0\) , \( a\) , \( 440 a + 1427\) , \( 4777 a + 15077\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(440a+1427\right){x}+4777a+15077$
450.3-q1 450.3-q \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.440475417$ 3.086984356 \( -\frac{7361303}{4860} a + \frac{9044707}{3888} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 65 a - 210\) , \( -465 a + 1467\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(65a-210\right){x}-465a+1467$
450.3-q2 450.3-q \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.610118854$ 3.086984356 \( \frac{20775046733269}{34867844010} a + \frac{361175517267013}{174339220050} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -385 a + 1140\) , \( 20035 a - 63533\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-385a+1140\right){x}+20035a-63533$
450.3-q3 450.3-q \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.220237708$ 3.086984356 \( \frac{184784183669}{118098} a + \frac{5854047089047}{1180980} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 265 a - 910\) , \( 3895 a - 12533\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(265a-910\right){x}+3895a-12533$
450.3-q4 450.3-q \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.305059427$ 3.086984356 \( \frac{37688339331809089}{2430} a + \frac{23836231835693689}{486} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 4115 a - 14160\) , \( 269195 a - 865933\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(4115a-14160\right){x}+269195a-865933$
450.3-r1 450.3-r \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.278486055$ $8.736672867$ 4.616371793 \( -\frac{533474309}{12} a + \frac{843496315}{6} \) \( \bigl[a\) , \( a\) , \( a\) , \( 40 a - 235\) , \( -145 a + 2210\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(40a-235\right){x}-145a+2210$
450.3-r2 450.3-r \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.092828685$ $2.912224289$ 4.616371793 \( -\frac{225727}{864} a + \frac{400355}{432} \) \( \bigl[1\) , \( a\) , \( a\) , \( 88 a + 282\) , \( -3126 a - 9888\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(88a+282\right){x}-3126a-9888$
450.3-s1 450.3-s \(\Q(\sqrt{10}) \) \( 2 \cdot 3^{2} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.763049502$ $1.578502414$ 4.570663091 \( \frac{1181545}{108} a - \frac{1128415}{27} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -9 a - 53\) , \( -24 a - 222\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-53\right){x}-24a-222$
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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.