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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
17500.2-a1 17500.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.653095700$ $0.995740051$ 1.966363334 \( -\frac{417267265}{235298} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -45\) , \( -185\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-45{x}-185$
17500.2-a2 17500.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.217698566$ $2.987220153$ 1.966363334 \( \frac{397535}{392} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 5\) , \( 5\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+5{x}+5$
17500.2-b1 17500.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.739989786$ 1.118759399 \( \frac{385902711}{8960} a - \frac{838409589}{4480} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -150 a - 17\) , \( -900 a + 641\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-150a-17\right){x}-900a+641$
17500.2-b2 17500.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.739989786$ 1.118759399 \( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 150 a - 167\) , \( 900 a - 259\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(150a-167\right){x}+900a-259$
17500.2-b3 17500.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.739989786$ 1.118759399 \( \frac{1367631}{2800} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 58\) , \( -284\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+58{x}-284$
17500.2-b4 17500.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.369994893$ 1.118759399 \( \frac{611960049}{122500} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -442\) , \( -2784\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-442{x}-2784$
17500.2-b5 17500.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.184997446$ 1.118759399 \( \frac{74565301329}{5468750} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -2192\) , \( 37466\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-2192{x}+37466$
17500.2-b6 17500.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.184997446$ 1.118759399 \( \frac{2121328796049}{120050} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -6692\) , \( -209034\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-6692{x}-209034$
17500.2-c1 17500.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $0.124475760$ 0.376379320 \( -\frac{1026590625}{100352} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -4492\) , \( 126416\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-4492{x}+126416$
17500.2-d1 17500.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.134936984$ 1.836049899 \( \frac{185012985079}{78400000} a - \frac{650824056453}{196000000} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 87 a + 2991\) , \( -55657 a + 43491\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(87a+2991\right){x}-55657a+43491$
17500.2-d2 17500.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.134936984$ 1.836049899 \( -\frac{9103345957169}{11239424000} a - \frac{4743040859549}{5619712000} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 837 a + 1749\) , \( -41832 a + 53336\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(837a+1749\right){x}-41832a+53336$
17500.2-d3 17500.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.404810952$ 1.836049899 \( -\frac{3747996503}{9175040} a + \frac{81235193761}{45875200} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -38 a - 259\) , \( 468 a - 1259\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38a-259\right){x}+468a-1259$
17500.2-d4 17500.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.044978994$ 1.836049899 \( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -47288 a + 36749\) , \( -2146207 a + 6589586\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-47288a+36749\right){x}-2146207a+6589586$
17500.2-d5 17500.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.404810952$ 1.836049899 \( -\frac{13113497519}{17920} a + \frac{6018146637}{17920} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 712 a - 501\) , \( -7207 a - 2414\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(712a-501\right){x}-7207a-2414$
17500.2-d6 17500.2-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.044978994$ 1.836049899 \( \frac{810722517917135481181}{23488102400} a + \frac{525145258848812643673}{11744051200} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 15712 a + 246741\) , \( -37365032 a + 24812241\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15712a+246741\right){x}-37365032a+24812241$
17500.2-e1 17500.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.404810952$ 1.836049899 \( \frac{13113497519}{17920} a - \frac{3547675441}{8960} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -713 a + 212\) , \( 7206 a - 9620\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-713a+212\right){x}+7206a-9620$
17500.2-e2 17500.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.134936984$ 1.836049899 \( \frac{9103345957169}{11239424000} a - \frac{2655632525181}{1605632000} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -838 a + 2587\) , \( 41831 a + 11505\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-838a+2587\right){x}+41831a+11505$
17500.2-e3 17500.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.134936984$ 1.836049899 \( -\frac{185012985079}{78400000} a - \frac{376583187511}{392000000} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -87 a + 3078\) , \( 55657 a - 12166\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-87a+3078\right){x}+55657a-12166$
17500.2-e4 17500.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.404810952$ 1.836049899 \( \frac{3747996503}{9175040} a + \frac{31247605623}{22937600} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 38 a - 297\) , \( -468 a - 791\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(38a-297\right){x}-468a-791$
17500.2-e5 17500.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.044978994$ 1.836049899 \( -\frac{41282203518025836237719}{630503947831869440} a + \frac{37460205421439226610825}{126100789566373888} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 47287 a - 10538\) , \( 2146206 a + 4443380\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(47287a-10538\right){x}+2146206a+4443380$
17500.2-e6 17500.2-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $0.044978994$ 1.836049899 \( -\frac{810722517917135481181}{23488102400} a + \frac{1861013035614760768527}{23488102400} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -15712 a + 262453\) , \( 37365032 a - 12552791\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-15712a+262453\right){x}+37365032a-12552791$
17500.2-f1 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.208472088$ $0.175083427$ 8.939617596 \( -\frac{548347731625}{1835008} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -4263\) , \( -109219\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-4263{x}-109219$
17500.2-f2 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $0.312708132$ $0.525250281$ 8.939617596 \( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) \( \bigl[1\) , \( a\) , \( a\) , \( 250 a + 153\) , \( 838 a - 3853\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(250a+153\right){x}+838a-3853$
17500.2-f3 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $0.312708132$ $0.525250281$ 8.939617596 \( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -251 a + 403\) , \( -839 a - 3015\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-251a+403\right){x}-839a-3015$
17500.2-f4 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $0.938124397$ $1.575750843$ 8.939617596 \( \frac{831875}{112} a - \frac{499125}{56} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 28\) , \( 36 a - 15\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+28\right){x}+36a-15$
17500.2-f5 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $0.938124397$ $1.575750843$ 8.939617596 \( -\frac{831875}{112} a - \frac{166375}{112} \) \( \bigl[1\) , \( a\) , \( a\) , \( 28\) , \( -37 a + 22\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+28{x}-37a+22$
17500.2-f6 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.876248795$ $1.575750843$ 8.939617596 \( -\frac{15625}{28} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( 31\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-13{x}+31$
17500.2-f7 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.625416265$ $0.525250281$ 8.939617596 \( \frac{9938375}{21952} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 112\) , \( -719\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+112{x}-719$
17500.2-f8 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $0.104236044$ $0.175083427$ 8.939617596 \( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) \( \bigl[1\) , \( a\) , \( a\) , \( -750 a - 222\) , \( 3213 a - 19478\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-750a-222\right){x}+3213a-19478$
17500.2-f9 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $0.104236044$ $0.175083427$ 8.939617596 \( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 749 a - 972\) , \( -3214 a - 16265\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(749a-972\right){x}-3214a-16265$
17500.2-f10 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $1.250832530$ $0.262625140$ 8.939617596 \( \frac{4956477625}{941192} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -888\) , \( -8719\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-888{x}-8719$
17500.2-f11 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $3.752497591$ $0.787875421$ 8.939617596 \( \frac{128787625}{98} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -263\) , \( 1531\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-263{x}+1531$
17500.2-f12 17500.2-f \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\Z/2\Z$ $0.416944176$ $0.087541713$ 8.939617596 \( \frac{2251439055699625}{25088} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -68263\) , \( -6893219\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-68263{x}-6893219$
17500.2-g1 17500.2-g \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $1$ $\mathsf{trivial}$ $0.012846808$ $0.622378800$ 8.776020521 \( -\frac{1026590625}{100352} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -180\) , \( 1047\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-180{x}+1047$
17500.2-h1 17500.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\mathsf{trivial}$ $1$ $0.199148010$ 5.419502837 \( -\frac{417267265}{235298} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -1138\) , \( -20858\bigr] \) ${y}^2+{x}{y}={x}^{3}-1138{x}-20858$
17500.2-h2 17500.2-h \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{4} \cdot 7 \) $0$ $\Z/3\Z$ $1$ $0.597444030$ 5.419502837 \( \frac{397535}{392} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 112\) , \( 392\bigr] \) ${y}^2+{x}{y}={x}^{3}+112{x}+392$
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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.