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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
6.1-a1 6.1-a \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 3.131417342 \( -\frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 361 a - 2327\) , \( -7786 a + 50451\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(361a-2327\right){x}-7786a+50451$
6.1-a2 6.1-a \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 3.131417342 \( -\frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 81 a - 512\) , \( 1192 a - 7734\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(81a-512\right){x}+1192a-7734$
6.1-a3 6.1-a \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.503252134$ 3.131417342 \( -\frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 6571 a - 42572\) , \( 752882 a - 4879242\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(6571a-42572\right){x}+752882a-4879242$
6.1-b1 6.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.470597059$ $1.751695888$ 3.434369660 \( \frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 15 a - 108\) , \( 220 a - 1443\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15a-108\right){x}+220a-1443$
6.1-b2 6.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.156865686$ $15.76526299$ 3.434369660 \( \frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -5 a + 27\) , \( -8 a + 57\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+27\right){x}-8a+57$
6.1-b3 6.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.470597059$ $15.76526299$ 3.434369660 \( \frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -15 a - 33\) , \( -8 a + 249\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a-33\right){x}-8a+249$
6.1-c1 6.1-c \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $9.351598892$ $1.751695888$ 2.527667452 \( -\frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -72 a - 486\) , \( -1492 a - 9762\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-72a-486\right){x}-1492a-9762$
6.1-c2 6.1-c \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $3.117199630$ $15.76526299$ 2.527667452 \( -\frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 8 a + 54\) , \( 12 a + 78\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+54\right){x}+12a+78$
6.1-c3 6.1-c \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $9.351598892$ $15.76526299$ 2.527667452 \( -\frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 48 a - 186\) , \( -148 a + 2574\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(48a-186\right){x}-148a+2574$
6.1-d1 6.1-d \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 1.043805780 \( \frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1451 a - 9341\) , \( 67294 a + 436248\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1451a-9341\right){x}+67294a+436248$
6.1-d2 6.1-d \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 1.043805780 \( \frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -331 a - 2081\) , \( -8430 a - 54492\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-331a-2081\right){x}-8430a-54492$
6.1-d3 6.1-d \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.503252134$ 1.043805780 \( \frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -26291 a - 170321\) , \( -5931590 a - 38440956\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-26291a-170321\right){x}-5931590a-38440956$
6.1-e1 6.1-e \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 3.131417342 \( \frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -361 a - 2327\) , \( 7786 a + 50451\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-361a-2327\right){x}+7786a+50451$
6.1-e2 6.1-e \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 3.131417342 \( \frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -81 a - 512\) , \( -1192 a - 7734\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-81a-512\right){x}-1192a-7734$
6.1-e3 6.1-e \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.503252134$ 3.131417342 \( \frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -6571 a - 42572\) , \( -752882 a - 4879242\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-6571a-42572\right){x}-752882a-4879242$
6.1-f1 6.1-f \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.470597059$ $1.751695888$ 3.434369660 \( -\frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -17 a - 108\) , \( -221 a - 1443\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-17a-108\right){x}-221a-1443$
6.1-f2 6.1-f \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.156865686$ $15.76526299$ 3.434369660 \( -\frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3 a + 27\) , \( 7 a + 57\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(3a+27\right){x}+7a+57$
6.1-f3 6.1-f \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.470597059$ $15.76526299$ 3.434369660 \( -\frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 13 a - 33\) , \( 7 a + 249\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(13a-33\right){x}+7a+249$
6.1-g1 6.1-g \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $9.351598892$ $1.751695888$ 2.527667452 \( \frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -973785 a - 6310804\) , \( -1206878846 a - 7821468799\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-973785a-6310804\right){x}-1206878846a-7821468799$
6.1-g2 6.1-g \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $3.117199630$ $15.76526299$ 2.527667452 \( \frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -218825 a - 1418104\) , \( 140749150 a + 912158801\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-218825a-1418104\right){x}+140749150a+912158801$
6.1-g3 6.1-g \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $9.351598892$ $15.76526299$ 2.527667452 \( \frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -17715825 a - 114811624\) , \( 103259966350 a + 669201066497\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-17715825a-114811624\right){x}+103259966350a+669201066497$
6.1-h1 6.1-h \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 1.043805780 \( -\frac{76452242473}{49152} a - \frac{82500763787}{8192} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -55140 a - 357339\) , \( 17768356 a + 115152129\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-55140a-357339\right){x}+17768356a+115152129$
6.1-h2 6.1-h \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $13.52926920$ 1.043805780 \( -\frac{10513825}{288} a + \frac{3785397}{16} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -100 a - 639\) , \( 64500 a + 418029\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-100a-639\right){x}+64500a+418029$
6.1-h3 6.1-h \(\Q(\sqrt{42}) \) \( 2 \cdot 3 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.503252134$ 1.043805780 \( -\frac{97620665254362025}{12} a + \frac{105442369719932349}{2} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 900 a + 5841\) , \( -1746500 a - 11318595\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(900a+5841\right){x}-1746500a-11318595$
9.1-a1 9.1-a \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.45138346$ $2.246907049$ 5.703781587 \( -\frac{873722816}{59049} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( 126 a - 747\) , \( 2090 a - 13389\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(126a-747\right){x}+2090a-13389$
9.1-a2 9.1-a \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.290276692$ $11.23453524$ 5.703781587 \( \frac{64}{9} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( 6 a + 33\) , \( 5 a + 135\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(6a+33\right){x}+5a+135$
9.1-a3 9.1-a \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.645138346$ $22.46907049$ 5.703781587 \( \frac{85184}{3} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 22 a - 129\) , \( -185 a + 1208\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(22a-129\right){x}-185a+1208$
9.1-a4 9.1-a \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $8.225691731$ $4.493814098$ 5.703781587 \( \frac{58591911104}{243} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 1942 a - 12609\) , \( 114655 a - 743032\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(1942a-12609\right){x}+114655a-743032$
9.1-b1 9.1-b \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.427518132$ $2.246907049$ 1.535043934 \( -\frac{873722816}{59049} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -478 a - 3093\) , \( -16373 a - 106088\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-478a-3093\right){x}-16373a-106088$
9.1-b2 9.1-b \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.885503626$ $11.23453524$ 1.535043934 \( \frac{64}{9} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2 a + 27\) , \( 67 a + 424\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(2a+27\right){x}+67a+424$
9.1-b3 9.1-b \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.442751813$ $22.46907049$ 1.535043934 \( \frac{85184}{3} \) \( \bigl[a\) , \( a\) , \( 1\) , \( a + 15\) , \( 2\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+15\right){x}+2$
9.1-b4 9.1-b \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.213759066$ $4.493814098$ 1.535043934 \( \frac{58591911104}{243} \) \( \bigl[a\) , \( a\) , \( 1\) , \( -479 a - 3105\) , \( -17595 a - 114028\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-479a-3105\right){x}-17595a-114028$
9.1-c1 9.1-c \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.427518132$ $2.246907049$ 1.535043934 \( -\frac{873722816}{59049} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -322650 a - 2090997\) , \( 269081541 a + 1743847704\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-322650a-2090997\right){x}+269081541a+1743847704$
9.1-c2 9.1-c \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.885503626$ $11.23453524$ 1.535043934 \( \frac{64}{9} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 1350 a + 8763\) , \( -1072179 a - 6948504\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(1350a+8763\right){x}-1072179a-6948504$
9.1-c3 9.1-c \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.442751813$ $22.46907049$ 1.535043934 \( \frac{85184}{3} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -3720 a - 24009\) , \( -308755 a - 2000780\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-3720a-24009\right){x}-308755a-2000780$
9.1-c4 9.1-c \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.213759066$ $4.493814098$ 1.535043934 \( \frac{58591911104}{243} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -327720 a - 2123769\) , \( 259525040 a + 1681914670\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-327720a-2123769\right){x}+259525040a+1681914670$
9.1-d1 9.1-d \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $16.45138346$ $2.246907049$ 5.703781587 \( -\frac{873722816}{59049} \) \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -127 a - 747\) , \( -2091 a - 13389\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-127a-747\right){x}-2091a-13389$
9.1-d2 9.1-d \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.290276692$ $11.23453524$ 5.703781587 \( \frac{64}{9} \) \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -7 a + 33\) , \( -6 a + 135\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-7a+33\right){x}-6a+135$
9.1-d3 9.1-d \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.645138346$ $22.46907049$ 5.703781587 \( \frac{85184}{3} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -22 a - 129\) , \( 185 a + 1208\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-22a-129\right){x}+185a+1208$
9.1-d4 9.1-d \(\Q(\sqrt{42}) \) \( 3^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $8.225691731$ $4.493814098$ 5.703781587 \( \frac{58591911104}{243} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -1942 a - 12609\) , \( -114655 a - 743032\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-1942a-12609\right){x}-114655a-743032$
14.1-a1 14.1-a \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $24.21346718$ 3.736219100 \( \frac{9930171131}{392} a - \frac{9193553137}{56} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 48 a - 204\) , \( -272 a + 1976\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(48a-204\right){x}-272a+1976$
14.1-a2 14.1-a \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $24.21346718$ 3.736219100 \( \frac{225}{14} a - \frac{169}{2} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 8 a + 56\) , \( 16 a + 112\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(8a+56\right){x}+16a+112$
14.1-b1 14.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $7.027708105$ 1.084398903 \( -\frac{548347731625}{1835008} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -35476 a - 229804\) , \( 9223680 a + 59776488\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-35476a-229804\right){x}+9223680a+59776488$
14.1-b2 14.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.027708105$ 1.084398903 \( -\frac{15625}{28} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -116 a - 644\) , \( -3360 a - 21560\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-116a-644\right){x}-3360a-21560$
14.1-b3 14.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $7.027708105$ 1.084398903 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 924 a + 6096\) , \( 67680 a + 438832\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(924a+6096\right){x}+67680a+438832$
14.1-b4 14.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $7.027708105$ 1.084398903 \( \frac{4956477625}{941192} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -7396 a - 47824\) , \( 708960 a + 4594800\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7396a-47824\right){x}+708960a+4594800$
14.1-b5 14.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.027708105$ 1.084398903 \( \frac{128787625}{98} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2196 a - 14124\) , \( -145440 a - 942344\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2196a-14124\right){x}-145440a-942344$
14.1-b6 14.1-b \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $7.027708105$ 1.084398903 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -567956 a - 3680684\) , \( 592166400 a + 3837677032\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-567956a-3680684\right){x}+592166400a+3837677032$
14.1-c1 14.1-c \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.484059793$ $7.027708105$ 3.778110619 \( -\frac{548347731625}{1835008} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -8871 a - 57416\) , \( 1135220 a + 7357190\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-8871a-57416\right){x}+1135220a+7357190$
14.1-c2 14.1-c \(\Q(\sqrt{42}) \) \( 2 \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.484059793$ $7.027708105$ 3.778110619 \( -\frac{15625}{28} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( -31 a - 126\) , \( -480 a - 2986\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-126\right){x}-480a-2986$
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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.