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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
19404.2-a1 19404.2-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $2.853951571$ $0.387270809$ 2.665968460 \( \frac{380239251435504673}{6263157401002656} a + \frac{6832513042456643645}{6263157401002656} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -163 a + 138\) , \( -715 a - 354\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-163a+138\right){x}-715a-354$
19404.2-b1 19404.2-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.311917496$ $2.430613929$ 3.657458092 \( \frac{85589351}{87318} a + \frac{41134283}{43659} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( a + 10\) , \( -7 a + 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+10\right){x}-7a+3$
19404.2-b2 19404.2-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.623834992$ $4.861227858$ 3.657458092 \( -\frac{1997423}{2772} a + \frac{3667757}{2772} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( a\) , \( -a + 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+a{x}-a+3$
19404.2-c1 19404.2-c \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $2.853951571$ $0.387270809$ 2.665968460 \( -\frac{380239251435504673}{6263157401002656} a + \frac{171732197473622579}{149122795261968} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 162 a - 24\) , \( 714 a - 1068\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(162a-24\right){x}+714a-1068$
19404.2-d1 19404.2-d \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.623834992$ $4.861227858$ 3.657458092 \( \frac{1997423}{2772} a + \frac{278389}{462} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -2\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}-2{x}$
19404.2-d2 19404.2-d \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.311917496$ $2.430613929$ 3.657458092 \( -\frac{85589351}{87318} a + \frac{55952639}{29106} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 8\) , \( 6 a + 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+8{x}+6a+4$
19404.2-e1 19404.2-e \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.039411059$ $0.316157574$ 1.262305984 \( -\frac{7347774183121}{6119866368} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -405\) , \( 4731\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-405{x}+4731$
19404.2-e2 19404.2-e \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.078822119$ $0.158078787$ 1.262305984 \( \frac{45637459887836881}{13417633152} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -7445\) , \( 244091\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-7445{x}+244091$
19404.2-f1 19404.2-f \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $2$ $\Z/4\Z$ $1.227246246$ $3.507744261$ 5.191863719 \( \frac{4657463}{3696} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+4{x}$
19404.2-f2 19404.2-f \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $0.306811561$ $1.753872130$ 5.191863719 \( \frac{498677257}{213444} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -16\) , \( -20\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-16{x}-20$
19404.2-f3 19404.2-f \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $2$ $\Z/2\Z$ $0.306811561$ $0.876936065$ 5.191863719 \( \frac{223980311017}{4278582} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -126\) , \( 486\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-126{x}+486$
19404.2-f4 19404.2-f \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $2$ $\Z/2\Z$ $1.227246246$ $0.876936065$ 5.191863719 \( \frac{1285429208617}{614922} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -226\) , \( -1406\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-226{x}-1406$
19404.2-g1 19404.2-g \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.430413517$ $1.737990332$ 3.608750846 \( \frac{9938375}{274428} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 5\) , \( -23\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+5{x}-23$
19404.2-g2 19404.2-g \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.860827034$ $0.868995166$ 3.608750846 \( \frac{129938649625}{7072758} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -105\) , \( -441\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-105{x}-441$
19404.2-h1 19404.2-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $0.068658501$ 3.312210756 \( -\frac{333345918055753}{72923718045024} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -1444\) , \( 410800\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-1444{x}+410800$
19404.2-h2 19404.2-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/4\Z$ $1$ $0.274634007$ 3.312210756 \( \frac{29609739866953}{15259926528} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -644\) , \( -2352\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-644{x}-2352$
19404.2-h3 19404.2-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.137317003$ 3.312210756 \( \frac{21184262604460873}{216872764416} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -5764\) , \( 164560\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-5764{x}+164560$
19404.2-h4 19404.2-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $0.068658501$ 3.312210756 \( \frac{86129359107301290313}{9166294368} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -92004\) , \( 10703088\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-92004{x}+10703088$
19404.2-i1 19404.2-i \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $0.199443353$ $2.058706290$ 4.951965467 \( \frac{504202537}{449064} a - \frac{92789275}{449064} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 6 a - 2\) , \( -7 a - 4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(6a-2\right){x}-7a-4$
19404.2-j1 19404.2-j \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\mathsf{trivial}$ $0.199443353$ $2.058706290$ 4.951965467 \( -\frac{504202537}{449064} a + \frac{68568877}{74844} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -7 a + 5\) , \( 7 a - 11\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-7a+5\right){x}+7a-11$
19404.2-k1 19404.2-k \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.225007147$ $0.029755661$ 8.397749354 \( -\frac{520203426765625}{11054534935707648} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1676\) , \( 5058506\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-1676{x}+5058506$
19404.2-k2 19404.2-k \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $0.112503573$ $0.014877830$ 8.397749354 \( \frac{10228636028672744397625}{167006381634183168} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -452236\) , \( 115355594\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-452236{x}+115355594$
19404.2-l1 19404.2-l \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $2.383427014$ $0.249083709$ 8.591956653 \( -\frac{61653281712625}{21875235228} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -823\) , \( -11611\bigr] \) ${y}^2+{x}{y}={x}^{3}-823{x}-11611$
19404.2-l2 19404.2-l \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/6\Z$ $0.794475671$ $0.747251128$ 8.591956653 \( \frac{50447927375}{39517632} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 77\) , \( 161\bigr] \) ${y}^2+{x}{y}={x}^{3}+77{x}+161$
19404.2-l3 19404.2-l \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/6\Z$ $0.397237835$ $0.373625564$ 8.591956653 \( \frac{5290763640625}{2291573592} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -363\) , \( 1305\bigr] \) ${y}^2+{x}{y}={x}^{3}-363{x}+1305$
19404.2-l4 19404.2-l \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $1$ $\Z/2\Z$ $1.191713507$ $0.124541854$ 8.591956653 \( \frac{312196988566716625}{25367712678} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -14133\) , \( -647829\bigr] \) ${y}^2+{x}{y}={x}^{3}-14133{x}-647829$
19404.2-m1 19404.2-m \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/4\Z$ $1$ $0.464791575$ 6.726716784 \( -\frac{100999381393}{723148272} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -97\) , \( 1337\bigr] \) ${y}^2+{x}{y}={x}^{3}-97{x}+1337$
19404.2-m2 19404.2-m \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $0.116197893$ 6.726716784 \( \frac{4770223741048753}{2740574865798} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -3507\) , \( 6507\bigr] \) ${y}^2+{x}{y}={x}^{3}-3507{x}+6507$
19404.2-m3 19404.2-m \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.232395787$ 6.726716784 \( \frac{1763535241378513}{4612311396} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -2517\) , \( 48285\bigr] \) ${y}^2+{x}{y}={x}^{3}-2517{x}+48285$
19404.2-m4 19404.2-m \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 3^{2} \cdot 7^{2} \cdot 11 \) $0$ $\Z/2\Z$ $1$ $0.116197893$ 6.726716784 \( \frac{7209828390823479793}{49509306} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -40247\) , \( 3104415\bigr] \) ${y}^2+{x}{y}={x}^{3}-40247{x}+3104415$
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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.