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Results (19 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
5324.7-a1 5324.7-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/3\Z$ $0.804718677$ $0.722336016$ 1.757617297 \( \frac{531165637}{1362944} a - \frac{402644615}{1362944} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 44 a - 37\) , \( 279 a - 159\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(44a-37\right){x}+279a-159$
5324.7-a2 5324.7-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $2.414156031$ $0.240778672$ 1.757617297 \( -\frac{4070378798731}{11811160064} a + \frac{4282573003625}{11811160064} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -396 a + 348\) , \( -6354 a + 6144\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-396a+348\right){x}-6354a+6144$
5324.7-b1 5324.7-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $0.036077686$ $4.305972120$ 3.288129422 \( -\frac{399175}{1408} a + \frac{2926837}{704} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -a + 2\) , \( a + 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-a+2\right){x}+a+2$
5324.7-c1 5324.7-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z$ $1.964954788$ $0.288454494$ 3.427684460 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 157 a + 140\) , \( 3795 a - 654\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(157a+140\right){x}+3795a-654$
5324.7-c2 5324.7-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/4\Z$ $0.245619348$ $0.288454494$ 3.427684460 \( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 48 a - 320\) , \( 3251 a + 758\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(48a-320\right){x}+3251a+758$
5324.7-c3 5324.7-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.491238697$ $0.288454494$ 3.427684460 \( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 537 a + 109\) , \( 192 a + 7744\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(537a+109\right){x}+192a+7744$
5324.7-c4 5324.7-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.982477394$ $0.288454494$ 3.427684460 \( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 307 a - 849\) , \( 4407 a - 7821\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(307a-849\right){x}+4407a-7821$
5324.7-c5 5324.7-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z$ $0.982477394$ $0.144227247$ 3.427684460 \( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 8297 a + 1789\) , \( 17536 a + 527872\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(8297a+1789\right){x}+17536a+527872$
5324.7-c6 5324.7-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z$ $1.964954788$ $0.144227247$ 3.427684460 \( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 4707 a - 13169\) , \( 291111 a - 525613\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(4707a-13169\right){x}+291111a-525613$
5324.7-d1 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 21 a - 64\) , \( -59 a + 50\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(21a-64\right){x}-59a+50$
5324.7-d2 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( \frac{46830231}{234256} a + \frac{377324919}{234256} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 39 a + 11\) , \( -46 a - 37\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(39a+11\right){x}-46a-37$
5324.7-d3 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.440785834$ 2.665622171 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 329 a + 211\) , \( -1214 a + 5583\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(329a+211\right){x}-1214a+5583$
5324.7-d4 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.440785834$ 2.665622171 \( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 131 a - 614\) , \( 1723 a - 5472\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(131a-614\right){x}+1723a-5472$
5324.7-d5 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 129 a + 23\) , \( 26 a + 989\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(129a+23\right){x}+26a+989$
5324.7-d6 5324.7-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) \( \bigl[1\) , \( -1\) , \( a\) , \( 75 a - 202\) , \( 547 a - 934\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(75a-202\right){x}+547a-934$
5324.7-e1 5324.7-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.482136211$ 2.240779327 \( \frac{704969}{484} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -14 a + 12\) , \( 15 a - 13\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-14a+12\right){x}+15a-13$
5324.7-e2 5324.7-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.741068105$ 2.240779327 \( \frac{59776471}{29282} \) \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 66 a - 58\) , \( 71 a + 59\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(66a-58\right){x}+71a+59$
5324.7-e3 5324.7-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $1.482136211$ 2.240779327 \( -\frac{34643161}{176} a + \frac{13683239}{88} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -7 a - 54\) , \( -59 a - 165\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a-54\right){x}-59a-165$
5324.7-e4 5324.7-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $1.482136211$ 2.240779327 \( \frac{34643161}{176} a - \frac{7276683}{176} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 16 a + 46\) , \( -130 a + 160\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(16a+46\right){x}-130a+160$
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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.