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Results (24 matches)

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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
375.2-a1 375.2-a \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.040625144$ $10.53250423$ 4.474559968 \( -\frac{208058}{75} a + \frac{33551}{25} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( a - 4\) , \( a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a-4\right){x}+a-1$
375.2-a2 375.2-a \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.520312572$ $5.266252119$ 4.474559968 \( \frac{14550280309}{1875} a + \frac{35641186181}{1875} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -34 a - 69\) , \( 112 a + 223\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-34a-69\right){x}+112a+223$
375.2-b1 375.2-b \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.373592794$ 1.096880035 \( -\frac{208058}{75} a + \frac{33551}{25} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 168 a - 410\) , \( -1498 a + 3669\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(168a-410\right){x}-1498a+3669$
375.2-b2 375.2-b \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.686796397$ 1.096880035 \( \frac{14550280309}{1875} a + \frac{35641186181}{1875} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( -247 a + 605\) , \( -8721 a + 21362\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(-247a+605\right){x}-8721a+21362$
375.2-c1 375.2-c \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $20.38989080$ 4.162069031 \( -\frac{81720253739776}{75} a + \frac{66724211524672}{25} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 1241 a - 3040\) , \( -37209 a + 91141\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1241a-3040\right){x}-37209a+91141$
375.2-c2 375.2-c \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.077978161$ 4.162069031 \( -\frac{8297016064}{263671875} a + \frac{155957523008}{87890625} \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 356 a + 870\) , \( -179 a - 439\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(356a+870\right){x}-179a-439$
375.2-c3 375.2-c \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.077978161$ 4.162069031 \( -\frac{109693837568}{759375} a + \frac{270029745088}{759375} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 11 a - 44\) , \( 59 a - 163\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(11a-44\right){x}+59a-163$
375.2-c4 375.2-c \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $20.38989080$ 4.162069031 \( \frac{45398592012032}{15} a + \frac{111203420137408}{15} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -329 a - 812\) , \( 5101 a + 12497\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-329a-812\right){x}+5101a+12497$
375.2-d1 375.2-d \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.517065719$ $0.905698896$ 2.039935193 \( -\frac{81720253739776}{75} a + \frac{66724211524672}{25} \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -72 a - 232\) , \( -582 a - 1712\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-72a-232\right){x}-582a-1712$
375.2-d2 375.2-d \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/10\Z$ $\mathrm{SU}(2)$ $1.103413143$ $4.528494481$ 2.039935193 \( -\frac{8297016064}{263671875} a + \frac{155957523008}{87890625} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 8 a - 4\) , \( 5 a + 4\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a-4\right){x}+5a+4$
375.2-d3 375.2-d \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/10\Z$ $\mathrm{SU}(2)$ $0.551706571$ $9.056988962$ 2.039935193 \( -\frac{109693837568}{759375} a + \frac{270029745088}{759375} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -357 a - 874\) , \( 178 a + 436\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-357a-874\right){x}+178a+436$
375.2-d4 375.2-d \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.758532859$ $1.811397792$ 2.039935193 \( \frac{45398592012032}{15} a + \frac{111203420137408}{15} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 308 a - 764\) , \( 4648 a - 11434\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(308a-764\right){x}+4648a-11434$
375.2-e1 375.2-e \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.83482297$ 3.232269705 \( -\frac{1075456}{75} a + \frac{877632}{25} \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( 13 a - 36\) , \( -40 a + 95\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(13a-36\right){x}-40a+95$
375.2-e2 375.2-e \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $15.83482297$ 3.232269705 \( \frac{143104}{5} a + \frac{1083328}{15} \) \( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -4 a - 6\) , \( -3 a - 7\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-6\right){x}-3a-7$
375.2-f1 375.2-f \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.127613823$ 2.762078493 \( -\frac{346213168567}{3645} a + \frac{848044778507}{3645} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -154 a - 387\) , \( -4879 a - 11963\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-154a-387\right){x}-4879a-11963$
375.2-f2 375.2-f \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.020910584$ 2.762078493 \( \frac{16292}{45} a + \frac{13591}{15} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -19 a - 47\) , \( -15 a - 37\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-19a-47\right){x}-15a-37$
375.2-f3 375.2-f \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.510455292$ 2.762078493 \( \frac{73011154}{675} a + \frac{193909061}{675} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -229 a - 562\) , \( -2969 a - 7273\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-229a-562\right){x}-2969a-7273$
375.2-f4 375.2-f \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.255227646$ 2.762078493 \( \frac{349197440831723}{5625} a + \frac{285118523163019}{1875} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 3117 a - 7635\) , \( -108499 a + 265765\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(3117a-7635\right){x}-108499a+265765$
375.2-g1 375.2-g \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.060493764$ $7.536433371$ 2.233480139 \( -\frac{346213168567}{3645} a + \frac{848044778507}{3645} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 185 a - 458\) , \( -2125 a + 5223\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(185a-458\right){x}-2125a+5223$
375.2-g2 375.2-g \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.241975057$ $15.07286674$ 2.233480139 \( \frac{16292}{45} a + \frac{13591}{15} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 2\) , \( -2 a + 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+2{x}-2a+5$
375.2-g3 375.2-g \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.120987528$ $15.07286674$ 2.233480139 \( \frac{73011154}{675} a + \frac{193909061}{675} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 10 a - 33\) , \( -30 a + 78\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(10a-33\right){x}-30a+78$
375.2-g4 375.2-g \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.241975057$ $7.536433371$ 2.233480139 \( \frac{349197440831723}{5625} a + \frac{285118523163019}{1875} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -5 a - 168\) , \( 273 a + 105\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-5a-168\right){x}+273a+105$
375.2-h1 375.2-h \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.188797424$ $16.84581154$ 1.298411572 \( -\frac{1075456}{75} a + \frac{877632}{25} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -a - 2\) , \( a + 2\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-2\right){x}+a+2$
375.2-h2 375.2-h \(\Q(\sqrt{6}) \) \( 3 \cdot 5^{3} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.094398712$ $33.69162308$ 1.298411572 \( \frac{143104}{5} a + \frac{1083328}{15} \) \( \bigl[a\) , \( -1\) , \( 1\) , \( 6 a - 16\) , \( -5 a + 12\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-16\right){x}-5a+12$
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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.