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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
61731.2-a1 61731.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $1.182529221$ $0.123884704$ 2.706567867 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( -36927 a + 48468\) , \( -1388304 a - 2608018\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-36927a+48468\right){x}-1388304a-2608018$
61731.2-a2 61731.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $1.182529221$ $0.123884704$ 2.706567867 \( \frac{14306161739497472}{322687697779} a - \frac{27123251845038080}{322687697779} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 19 a + 6700\) , \( -244436 a + 127622\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(19a+6700\right){x}-244436a+127622$
61731.2-a3 61731.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $1.182529221$ $0.123884704$ 2.706567867 \( -\frac{14306161739497472}{322687697779} a - \frac{12817090105540608}{322687697779} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 4309 a - 7730\) , \( 192094 a - 234274\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4309a-7730\right){x}+192094a-234274$
61731.2-a4 61731.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $0.394176407$ $0.371654113$ 2.706567867 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 589 a - 140\) , \( -1616 a - 3991\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(589a-140\right){x}-1616a-3991$
61731.2-a5 61731.2-a \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $1$ $\mathsf{trivial}$ $0.131392135$ $1.114962340$ 2.706567867 \( \frac{32768}{19} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 11 a + 32\) , \( 16 a + 4\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(11a+32\right){x}+16a+4$
61731.2-b1 61731.2-b \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $0.108104655$ 0.998628029 \( \frac{7240152655469734}{50950689123} a - \frac{5512832666599067}{50950689123} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 11237 a - 5950\) , \( 322105 a + 82626\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(11237a-5950\right){x}+322105a+82626$
61731.2-b2 61731.2-b \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.216209310$ 0.998628029 \( \frac{67419143}{390963} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 407 a - 535\) , \( 4786 a + 8982\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(407a-535\right){x}+4786a+8982$
61731.2-b3 61731.2-b \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $0.864837242$ 0.998628029 \( \frac{389017}{57} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -73 a + 95\) , \( -104 a - 168\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-73a+95\right){x}-104a-168$
61731.2-b4 61731.2-b \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.432418621$ 0.998628029 \( \frac{30664297}{3249} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -313 a + 410\) , \( 979 a + 1998\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-313a+410\right){x}+979a+1998$
61731.2-b5 61731.2-b \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $0.108104655$ 0.998628029 \( -\frac{7240152655469734}{50950689123} a + \frac{1727319988870667}{50950689123} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 1097 a - 10240\) , \( -68165 a + 397614\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(1097a-10240\right){x}-68165a+397614$
61731.2-b6 61731.2-b \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $0.216209310$ 0.998628029 \( \frac{115714886617}{1539} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -4873 a + 6395\) , \( 66244 a + 128538\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-4873a+6395\right){x}+66244a+128538$
61731.2-c1 61731.2-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $0.539045766$ 1.244872874 \( \frac{363527109}{361} a - \frac{76135923}{361} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 601 a - 417\) , \( 4772 a - 273\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(601a-417\right){x}+4772a-273$
61731.2-c2 61731.2-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $0.539045766$ 1.244872874 \( \frac{36038181633}{47045881} a - \frac{75585143946}{47045881} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -a - 145\) , \( -222 a - 909\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-a-145\right){x}-222a-909$
61731.2-c3 61731.2-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $1.078091533$ 1.244872874 \( -\frac{29840721}{6859} a - \frac{5426511}{6859} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -56 a + 40\) , \( 81 a - 156\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-56a+40\right){x}+81a-156$
61731.2-c4 61731.2-c \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $1.078091533$ 1.244872874 \( \frac{9153}{19} a + \frac{27648}{19} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 46 a - 27\) , \( 44 a - 24\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(46a-27\right){x}+44a-24$
61731.2-d1 61731.2-d \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.035996263$ 0.831298097 \( -\frac{9358714467168256}{22284891} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 276592 a - 65855\) , \( -18648239 a - 36055987\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(276592a-65855\right){x}-18648239a-36055987$
61731.2-d2 61731.2-d \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.179981317$ 0.831298097 \( \frac{841232384}{1121931} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( -1238 a + 295\) , \( -7169 a - 11797\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1238a+295\right){x}-7169a-11797$
61731.2-e1 61731.2-e \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.371111235$ 1.714089374 \( \frac{1024000}{513} a - \frac{2560000}{513} \) \( \bigl[0\) , \( a + 1\) , \( 1\) , \( -84 a + 450\) , \( 4386 a - 1174\bigr] \) ${y}^2+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-84a+450\right){x}+4386a-1174$
61731.2-f1 61731.2-f \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\mathsf{trivial}$ $1$ $0.705796155$ 3.259932801 \( -\frac{1404928}{171} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 148 a - 35\) , \( 167 a + 545\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(148a-35\right){x}+167a+545$
61731.2-g1 61731.2-g \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $1$ $\Z/2\Z$ $1.384520053$ $0.712333856$ 4.555249792 \( -\frac{61536}{361} a + \frac{21201}{361} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 42 a - 44\) , \( -343 a - 51\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(42a-44\right){x}-343a-51$
61731.2-g2 61731.2-g \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $1$ $\Z/2\Z$ $2.769040107$ $0.356166928$ 4.555249792 \( -\frac{5845799184}{130321} a + \frac{1712734635}{130321} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -238 a - 579\) , \( -3795 a - 5177\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-238a-579\right){x}-3795a-5177$
61731.2-h1 61731.2-h \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $1.792667560$ 4.139988395 \( -\frac{61536}{361} a + \frac{21201}{361} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -7 a - 1\) , \( 15 a + 9\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-1\right){x}+15a+9$
61731.2-h2 61731.2-h \(\Q(\sqrt{-3}) \) \( 3^{2} \cdot 19^{3} \) $0$ $\Z/2\Z$ $1$ $0.896333780$ 4.139988395 \( -\frac{5845799184}{130321} a + \frac{1712734635}{130321} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -112 a + 119\) , \( 6 a + 459\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-112a+119\right){x}+6a+459$
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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.