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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
4.1-a1 4.1-a \(\Q(\sqrt{313}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.088720921$ 1.128330672 \( -\frac{7762509612594001}{8} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 15009962115660926840 a - 140281650063862322521\) , \( 94146372725548684750220817720 a - 879882867904615924996270935249\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(15009962115660926840a-140281650063862322521\right){x}+94146372725548684750220817720a-879882867904615924996270935249$
4.1-a2 4.1-a \(\Q(\sqrt{313}) \) \( 2^{2} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $2.218023042$ 1.128330672 \( -\frac{13997521}{32768} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -18269609092248440 a - 152476385450157001\) , \( -8979833730671276656374200 a - 74944821330473578057889289\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-18269609092248440a-152476385450157001\right){x}-8979833730671276656374200a-74944821330473578057889289$
6.1-a1 6.1-a \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.942073802$ 9.312567232 \( -\frac{17885764951}{839808} a - \frac{149237511971}{839808} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( -983519970721626 a - 8208362280575830\) , \( -50049833920803194060535 a - 417711059393309230996834\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-983519970721626a-8208362280575830\right){x}-50049833920803194060535a-417711059393309230996834$
6.1-b1 6.1-b \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $53.18837060$ 3.006384456 \( -\frac{61860289}{36} a + \frac{576972199}{36} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -37407 a - 312191\) , \( 12017370 a + 100295787\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-37407a-312191\right){x}+12017370a+100295787$
6.1-b2 6.1-b \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $53.18837060$ 3.006384456 \( \frac{373461059}{6} a + \frac{3116840965}{6} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -6\) , \( -a - 12\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-6{x}-a-12$
6.2-a1 6.2-a \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $8.475854132$ 0.479083600 \( -\frac{231358159735}{1417176} a + \frac{719533421119}{472392} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 13826 a - 129175\) , \( -2536295 a + 23704109\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13826a-129175\right){x}-2536295a+23704109$
6.2-b1 6.2-b \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.090717984$ $18.77386760$ 2.502927816 \( -\frac{155033667913}{12754584} a - \frac{445409678207}{4251528} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 5143583738317716 a - 48071434724010025\) , \( -736452672543977709228199 a + 6882815246456831671895385\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5143583738317716a-48071434724010025\right){x}-736452672543977709228199a+6882815246456831671895385$
6.2-c1 6.2-c \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.902412291$ $7.363990971$ 2.253706363 \( \frac{3966815}{24} a - \frac{12344039}{8} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 169647785224059 a - 1585511745967624\) , \( 3578367908069622245487 a - 33443079390308932843957\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(169647785224059a-1585511745967624\right){x}+3578367908069622245487a-33443079390308932843957$
6.2-d1 6.2-d \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $10.21126003$ 1.731523625 \( -\frac{21389534721775}{7962624} a - \frac{59180172859913}{2654208} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -57339913824558 a - 478553359179337\) , \( 702954879944245916135 a + 5866793245944407169255\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-57339913824558a-478553359179337\right){x}+702954879944245916135a+5866793245944407169255$
6.2-d2 6.2-d \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.408450401$ 1.731523625 \( -\frac{36117318693345370853625055}{24} a + \frac{112516319120675616097055847}{8} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 247523046194992 a + 2065803335411323\) , \( 2986500215715667636925 a + 24925041129185797501155\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(247523046194992a+2065803335411323\right){x}+2986500215715667636925a+24925041129185797501155$
6.2-e1 6.2-e \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $23.50060612$ 1.328332794 \( -\frac{3941125}{36864} a + \frac{11756125}{12288} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 2527377 a - 23620591\) , \( -1657479982 a + 15490647087\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2527377a-23620591\right){x}-1657479982a+15490647087$
6.2-e2 6.2-e \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $23.50060612$ 1.328332794 \( \frac{56708125}{5184} a + \frac{160548875}{1728} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -4814374006498 a + 44994672501664\) , \( -4548671843351188043 a + 42511445856253447310\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4814374006498a+44994672501664\right){x}-4548671843351188043a+42511445856253447310$
6.2-f1 6.2-f \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.213608567$ $39.15311215$ 2.836377535 \( -\frac{63007}{216} a + \frac{193447}{72} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 10 a + 157\) , \( 38 a + 429\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(10a+157\right){x}+38a+429$
6.3-a1 6.3-a \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $8.475854132$ 0.479083600 \( \frac{231358159735}{1417176} a + \frac{963621051811}{708588} \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( -13828 a - 115348\) , \( 2536294 a + 21167814\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-13828a-115348\right){x}+2536294a+21167814$
6.3-b1 6.3-b \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.090717984$ $18.77386760$ 2.502927816 \( \frac{155033667913}{12754584} a - \frac{745631351267}{6377292} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -5143583738317718 a - 42927850985692308\) , \( 736452672543977709228198 a + 6146362573912853962667186\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-5143583738317718a-42927850985692308\right){x}+736452672543977709228198a+6146362573912853962667186$
6.3-c1 6.3-c \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.902412291$ $7.363990971$ 2.253706363 \( -\frac{3966815}{24} a - \frac{16532651}{12} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( -169647785224060 a - 1415863960743564\) , \( -3578367908069622245487 a - 29864711482239310598470\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-169647785224060a-1415863960743564\right){x}-3578367908069622245487a-29864711482239310598470$
6.3-d1 6.3-d \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $10.21126003$ 1.731523625 \( \frac{21389534721775}{7962624} a - \frac{99465026650757}{3981312} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 57339913824557 a - 535893273003894\) , \( -702954879944245916135 a + 6569748125888653085390\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(57339913824557a-535893273003894\right){x}-702954879944245916135a+6569748125888653085390$
6.3-d2 6.3-d \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.408450401$ 1.731523625 \( \frac{36117318693345370853625055}{24} a + \frac{150715819334340738718771243}{12} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -247523046194993 a + 2313326381606316\) , \( -2986500215715667636925 a + 27911541344901465138080\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-247523046194993a+2313326381606316\right){x}-2986500215715667636925a+27911541344901465138080$
6.3-e1 6.3-e \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $23.50060612$ 1.328332794 \( -\frac{56708125}{5184} a + \frac{269177375}{2592} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 4814374006499 a + 40180298495166\) , \( 4548676657725194541 a + 37962814193200754433\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4814374006499a+40180298495166\right){x}+4548676657725194541a+37962814193200754433$
6.3-e2 6.3-e \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $23.50060612$ 1.328332794 \( \frac{3941125}{36864} a + \frac{15663625}{18432} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -2527376 a - 21093214\) , \( 1654952605 a + 13812073891\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2527376a-21093214\right){x}+1654952605a+13812073891$
6.3-f1 6.3-f \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.213608567$ $39.15311215$ 2.836377535 \( \frac{63007}{216} a + \frac{258667}{108} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -10 a + 89\) , \( -29 a + 300\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-10a+89\right){x}-29a+300$
6.4-a1 6.4-a \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.942073802$ 9.312567232 \( \frac{17885764951}{839808} a - \frac{27853879487}{139968} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( 983519970721626 a - 9191882251297456\) , \( 50049833920803194060535 a - 467760893314112425057369\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(983519970721626a-9191882251297456\right){x}+50049833920803194060535a-467760893314112425057369$
6.4-b1 6.4-b \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $53.18837060$ 3.006384456 \( -\frac{373461059}{6} a + 581717004 \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -a - 6\) , \( -13\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-6\right){x}-13$
6.4-b2 6.4-b \(\Q(\sqrt{313}) \) \( 2 \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $53.18837060$ 3.006384456 \( \frac{61860289}{36} a + \frac{85851985}{6} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 37406 a - 349598\) , \( -12017371 a + 112313157\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(37406a-349598\right){x}-12017371a+112313157$
8.1-a1 8.1-a \(\Q(\sqrt{313}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $4.787043784$ $4.496135641$ 2.433126178 \( -\frac{2188125793}{128} a - \frac{9252435989}{64} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 280745939363330 a - 2623824318751957\) , \( -7619068073651398925377 a + 71207071216092039025495\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(280745939363330a-2623824318751957\right){x}-7619068073651398925377a+71207071216092039025495$
8.1-a2 8.1-a \(\Q(\sqrt{313}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.595681261$ $4.496135641$ 2.433126178 \( -\frac{27153241}{2097152} a - \frac{58274669}{1048576} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -789534123 a - 6589375007\) , \( -117958540081757 a - 984470534307289\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-789534123a-6589375007\right){x}-117958540081757a-984470534307289$
8.2-a1 8.2-a \(\Q(\sqrt{313}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $4.787043784$ $4.496135641$ 2.433126178 \( \frac{2188125793}{128} a - \frac{20692997771}{128} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -280745939363332 a - 2343078379388627\) , \( 7619068073651398925376 a + 63588003142440640100118\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-280745939363332a-2343078379388627\right){x}+7619068073651398925376a+63588003142440640100118$
8.2-a2 8.2-a \(\Q(\sqrt{313}) \) \( 2^{3} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.595681261$ $4.496135641$ 2.433126178 \( \frac{27153241}{2097152} a - \frac{143702579}{2097152} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 789534121 a - 7378909130\) , \( 117958540081756 a - 1102429074389046\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(789534121a-7378909130\right){x}+117958540081756a-1102429074389046$
9.1-a1 9.1-a \(\Q(\sqrt{313}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.240334716$ $12.47806199$ 1.749620528 \( -\frac{4096}{27} a + \frac{4096}{9} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 18\) , \( -3 a - 40\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+18{x}-3a-40$
9.1-b1 9.1-b \(\Q(\sqrt{313}) \) \( 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.011005096$ 0.283238754 \( -\frac{5071288251250}{43046721} a + \frac{47395768139125}{43046721} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 3290 a - 30748\) , \( 306756 a - 2866912\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(3290a-30748\right){x}+306756a-2866912$
9.1-b2 9.1-b \(\Q(\sqrt{313}) \) \( 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $20.04402038$ 0.283238754 \( -\frac{12244521250}{81} a + \frac{38145403375}{27} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 400128170 a + 3339430897\) , \( -7882451771672 a - 65786177939608\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(400128170a+3339430897\right){x}-7882451771672a-65786177939608$
9.1-b3 9.1-b \(\Q(\sqrt{313}) \) \( 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $20.04402038$ 0.283238754 \( -\frac{18590000}{6561} a + \frac{63018875}{2187} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -240 a - 2003\) , \( -3168 a - 26440\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-240a-2003\right){x}-3168a-26440$
9.1-b4 9.1-b \(\Q(\sqrt{313}) \) \( 3^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $20.04402038$ 0.283238754 \( \frac{18590000}{6561} a + \frac{170466625}{6561} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 240 a - 2243\) , \( 3168 a - 29608\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(240a-2243\right){x}+3168a-29608$
9.1-b5 9.1-b \(\Q(\sqrt{313}) \) \( 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.011005096$ 0.283238754 \( \frac{5071288251250}{43046721} a + \frac{14108159962625}{14348907} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -3290 a - 27458\) , \( -306756 a - 2560156\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3290a-27458\right){x}-306756a-2560156$
9.1-b6 9.1-b \(\Q(\sqrt{313}) \) \( 3^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $20.04402038$ 0.283238754 \( \frac{12244521250}{81} a + \frac{102191688875}{81} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -400128170 a + 3739559067\) , \( 7882451771672 a - 73668629711280\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-400128170a+3739559067\right){x}+7882451771672a-73668629711280$
9.1-c1 9.1-c \(\Q(\sqrt{313}) \) \( 3^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1.240334716$ $12.47806199$ 1.749620528 \( \frac{4096}{27} a + \frac{8192}{27} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 2 a + 17\) , \( 2 a - 60\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+17\right){x}+2a-60$
12.1-a1 12.1-a \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.172320280$ $11.18429546$ 13.07236307 \( -\frac{43728727}{294912} a - \frac{330648227}{294912} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -24495034424 a - 204433181443\) , \( 8066815305981780 a + 67324858114888553\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-24495034424a-204433181443\right){x}+8066815305981780a+67324858114888553$
12.1-a2 12.1-a \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.057440093$ $11.18429546$ 13.07236307 \( \frac{3517297}{46656} a + \frac{369554}{729} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 334039188424 a - 3121897855373\) , \( -1215978224562060848 a + 11364414544745209713\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(334039188424a-3121897855373\right){x}-1215978224562060848a+11364414544745209713$
12.1-b1 12.1-b \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.840987243$ 4.431988027 \( -\frac{12725569}{9216} a + \frac{131569639}{9216} \) \( \bigl[1\) , \( a\) , \( 0\) , \( a + 25\) , \( 3 a + 15\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(a+25\right){x}+3a+15$
12.1-b2 12.1-b \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.840987243$ 4.431988027 \( \frac{23892007}{196608} a + \frac{100778515}{98304} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -62105 a + 580458\) , \( 313660985 a - 2931445110\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-62105a+580458\right){x}+313660985a-2931445110$
12.1-c1 12.1-c \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.537823388$ $3.581631886$ 6.165260345 \( -\frac{62850287725}{191102976} a - \frac{84359222897}{191102976} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 410 a - 3836\) , \( -6559 a + 61278\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(410a-3836\right){x}-6559a+61278$
12.1-c2 12.1-c \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.075646776$ $3.581631886$ 6.165260345 \( \frac{110648248535}{110592} a + \frac{464737746791}{55296} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 1570952240 a - 14681967267\) , \( 99190866050446 a - 927028213235949\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1570952240a-14681967267\right){x}+99190866050446a-927028213235949$
12.1-d1 12.1-d \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $7.704140248$ 0.435463753 \( \frac{57406005709}{497664} a - \frac{268255589879}{248832} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -32863692 a - 274277151\) , \( -19140935357199 a - 159748389944415\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-32863692a-274277151\right){x}-19140935357199a-159748389944415$
12.1-e1 12.1-e \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.752914472$ $11.94453905$ 2.033306563 \( -\frac{537107989}{576} a + \frac{2509875887}{288} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -3096086662677 a - 25839638986350\) , \( 102699774300421667218 a + 857122355098405338106\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-3096086662677a-25839638986350\right){x}+102699774300421667218a+857122355098405338106$
12.1-e2 12.1-e \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.250971490$ $11.94453905$ 2.033306563 \( -\frac{5665741}{46656} a + \frac{53547295}{46656} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 645122677 a - 6029253967\) , \( -11876625521538 a + 110997790168544\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(645122677a-6029253967\right){x}-11876625521538a+110997790168544$
12.1-e3 12.1-e \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.501942981$ $23.88907810$ 2.033306563 \( -\frac{37240843}{432} a + \frac{89698237}{108} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 4275289848755191 a - 39956444251042022\) , \( -452314306357488759071486 a + 4227285635659043004554630\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(4275289848755191a-39956444251042022\right){x}-452314306357488759071486a+4227285635659043004554630$
12.1-e4 12.1-e \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.505828944$ $23.88907810$ 2.033306563 \( \frac{84053687}{12288} a + \frac{380583395}{6144} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -18522321 a - 154585495\) , \( 128165281666 a + 1069655009582\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-18522321a-154585495\right){x}+128165281666a+1069655009582$
12.1-f1 12.1-f \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.522505830$ 3.849672405 \( -\frac{7790262311}{10077696} a - \frac{65014847347}{10077696} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -1430190 a - 11936227\) , \( -2939342474 a - 24531467191\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-1430190a-11936227\right){x}-2939342474a-24531467191$
12.2-a1 12.2-a \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.057440093$ $11.18429546$ 13.07236307 \( -\frac{3517297}{46656} a + \frac{9056251}{15552} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -334039188424 a - 2787858666949\) , \( 1215978224562060848 a + 10148436320183148865\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-334039188424a-2787858666949\right){x}+1215978224562060848a+10148436320183148865$
12.2-a2 12.2-a \(\Q(\sqrt{313}) \) \( 2^{2} \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.172320280$ $11.18429546$ 13.07236307 \( \frac{43728727}{294912} a - \frac{62396159}{49152} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 24495034424 a - 228928215867\) , \( -8066815305981780 a + 75391673420870333\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(24495034424a-228928215867\right){x}-8066815305981780a+75391673420870333$
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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.