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Results (36 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
512.2-a1 512.2-a \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $16.65604516$ 2.019842162 \( -1088 a + 2816 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( a + 2\) , \( 2 a + 3\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(a+2\right){x}+2a+3$
512.2-a2 512.2-a \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $16.65604516$ 2.019842162 \( -53387236 a + 136758060 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 75 a - 191\) , \( -546 a + 1398\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(75a-191\right){x}-546a+1398$
512.2-a3 512.2-a \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $33.31209033$ 2.019842162 \( 1008 a + 17168 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 5 a - 11\) , \( -10 a + 26\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(5a-11\right){x}-10a+26$
512.2-a4 512.2-a \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/4\Z$ $1$ $16.65604516$ 2.019842162 \( 87515172 a + 136659620 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -5 a + 9\) , \( -30 a + 78\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-5a+9\right){x}-30a+78$
512.2-b1 512.2-b \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/4\Z$ $0.495413934$ $11.52843721$ 2.770410930 \( -404500 a + 1037028 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 136 a - 344\) , \( -1200 a + 3072\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(136a-344\right){x}-1200a+3072$
512.2-b2 512.2-b \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.990827869$ $23.05687443$ 2.770410930 \( 240 a + 2576 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11 a - 24\) , \( -10 a + 24\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-24\right){x}-10a+24$
512.2-b3 512.2-b \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.495413934$ $23.05687443$ 2.770410930 \( 6168 a + 10976 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+{x}$
512.2-b4 512.2-b \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $1.981655739$ $5.764218608$ 2.770410930 \( 1335292 a + 2147084 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 81 a - 204\) , \( 568 a - 1456\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(81a-204\right){x}+568a-1456$
512.2-c1 512.2-c \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $15.16812741$ 1.839405631 \( -23360 a + 59136 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5 a - 9\) , \( 6 a - 14\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(5a-9\right){x}+6a-14$
512.2-c2 512.2-c \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $15.16812741$ 1.839405631 \( 414800 a + 647728 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 11 a - 24\) , \( 510 a - 1308\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(11a-24\right){x}+510a-1308$
512.2-d1 512.2-d \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $8.009701860$ 1.942638047 \( 184 a + 560 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 5\) , \( 2 a - 6\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-a+5\right){x}+2a-6$
512.2-d2 512.2-d \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.01940372$ 1.942638047 \( -1092 a + 5588 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -9 a - 12\) , \( -8 a - 12\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-9a-12\right){x}-8a-12$
512.2-d3 512.2-d \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $8.009701860$ 1.942638047 \( -10297338 a + 26411786 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -59 a - 92\) , \( 378 a + 588\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-59a-92\right){x}+378a+588$
512.2-d4 512.2-d \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $8.009701860$ 1.942638047 \( 910322 a + 1430310 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -124 a - 192\) , \( -1012 a - 1580\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-124a-192\right){x}-1012a-1580$
512.2-e1 512.2-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $6.239280630$ 1.513247827 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -8 a + 20\bigr] \) ${y}^2={x}^{3}+{x}^{2}-8a+20$
512.2-e2 512.2-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/4\Z$ $1$ $12.47856126$ 1.513247827 \( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -104 a - 168\) , \( 192 a + 304\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-104a-168\right){x}+192a+304$
512.2-e3 512.2-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $12.47856126$ 1.513247827 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -69 a - 108\) , \( -374 a - 584\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-69a-108\right){x}-374a-584$
512.2-e4 512.2-e \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $3.119640315$ 1.513247827 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 768 a - 1968\) , \( 7764 a - 19888\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(768a-1968\right){x}+7764a-19888$
512.2-f1 512.2-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.235830817$ $12.22307372$ 2.796510914 \( -\frac{217}{16} a - \frac{339}{16} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -5 a - 7\) , \( 50 a + 78\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-5a-7\right){x}+50a+78$
512.2-f2 512.2-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.235830817$ $12.22307372$ 2.796510914 \( -\frac{1592342311}{2} a + \frac{4078872403}{2} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 90 a - 235\) , \( -633 a + 1626\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(90a-235\right){x}-633a+1626$
512.2-f3 512.2-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.471661635$ $24.44614744$ 2.796510914 \( \frac{159495}{4} a + \frac{481229}{4} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 5 a - 15\) , \( -6 a + 22\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(5a-15\right){x}-6a+22$
512.2-f4 512.2-f \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.943323270$ $12.22307372$ 2.796510914 \( \frac{23841914775}{2} a + \frac{37230413581}{2} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -5 a - 55\) , \( 90 a + 54\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-5a-55\right){x}+90a+54$
512.2-g1 512.2-g \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $1.156172055$ $9.650305188$ 2.706070181 \( 184 a + 560 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a + 8\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(5a+8\right){x}$
512.2-g2 512.2-g \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.578086027$ $19.30061037$ 2.706070181 \( -1092 a + 5588 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 3 a - 4\) , \( 2 a - 4\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(3a-4\right){x}+2a-4$
512.2-g3 512.2-g \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $1.156172055$ $4.825152594$ 2.706070181 \( -10297338 a + 26411786 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 33 a - 84\) , \( 140 a - 364\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(33a-84\right){x}+140a-364$
512.2-g4 512.2-g \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/4\Z$ $0.289043013$ $19.30061037$ 2.706070181 \( 910322 a + 1430310 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 8 a - 24\) , \( -20 a + 52\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(8a-24\right){x}-20a+52$
512.2-h1 512.2-h \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.818306195$ $6.640608214$ 2.635901835 \( -23360 a + 59136 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -7 a - 9\) , \( -22 a - 34\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a-9\right){x}-22a-34$
512.2-h2 512.2-h \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $1.636612390$ $6.640608214$ 2.635901835 \( 414800 a + 647728 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( -4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}-a{x}-4$
512.2-i1 512.2-i \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/4\Z$ $0.399642117$ $14.24941430$ 2.762318808 \( -404500 a + 1037028 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a\) , \( 16\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+4a{x}+16$
512.2-i2 512.2-i \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.799284235$ $28.49882861$ 2.762318808 \( 240 a + 2576 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -a\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}-a{x}$
512.2-i3 512.2-i \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $1.598568471$ $14.24941430$ 2.762318808 \( 6168 a + 10976 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -14 a + 38\) , \( -15 a + 39\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-14a+38\right){x}-15a+39$
512.2-i4 512.2-i \(\Q(\sqrt{17}) \) \( 2^{9} \) $1$ $\Z/2\Z$ $0.399642117$ $14.24941430$ 2.762318808 \( 1335292 a + 2147084 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -11 a - 20\) , \( 26 a + 40\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a-20\right){x}+26a+40$
512.2-j1 512.2-j \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $10.62255413$ 1.288173903 \( -1088 a + 2816 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a - 15\) , \( 7 a - 18\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(6a-15\right){x}+7a-18$
512.2-j2 512.2-j \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/4\Z$ $1$ $21.24510827$ 1.288173903 \( -53387236 a + 136758060 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 28\) , \( 20 a + 36\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a-28\right){x}+20a+36$
512.2-j3 512.2-j \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $21.24510827$ 1.288173903 \( 1008 a + 17168 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( -18 a - 28\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-5a-8\right){x}-18a-28$
512.2-j4 512.2-j \(\Q(\sqrt{17}) \) \( 2^{9} \) $0$ $\Z/2\Z$ $1$ $5.311277067$ 1.288173903 \( 87515172 a + 136659620 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -95 a - 148\) , \( -848 a - 1324\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-95a-148\right){x}-848a-1324$
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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.