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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
5324.6-a1 5324.6-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/3\Z$ $0.804718677$ $0.722336016$ 1.757617297 \( -\frac{531165637}{1362944} a + \frac{64260511}{681472} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -45 a + 7\) , \( -280 a + 120\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-45a+7\right){x}-280a+120$
5324.6-a2 5324.6-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $2.414156031$ $0.240778672$ 1.757617297 \( \frac{4070378798731}{11811160064} a + \frac{106097102447}{5905580032} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 395 a - 48\) , \( 6353 a - 210\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(395a-48\right){x}+6353a-210$
5324.6-b1 5324.6-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.482136211$ 2.240779327 \( \frac{704969}{484} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 16 a - 2\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(16a-2\right){x}$
5324.6-b2 5324.6-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.741068105$ 2.240779327 \( \frac{59776471}{29282} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -64 a + 8\) , \( -136 a + 138\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-64a+8\right){x}-136a+138$
5324.6-b3 5324.6-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $1.482136211$ 2.240779327 \( -\frac{34643161}{176} a + \frac{13683239}{88} \) \( \bigl[1\) , \( a - 1\) , \( 0\) , \( -16 a + 62\) , \( 130 a + 30\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-16a+62\right){x}+130a+30$
5324.6-b4 5324.6-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $1.482136211$ 2.240779327 \( \frac{34643161}{176} a - \frac{7276683}{176} \) \( \bigl[1\) , \( -a - 1\) , \( 0\) , \( 9 a - 62\) , \( 51 a - 162\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-62\right){x}+51a-162$
5324.6-c1 5324.6-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\mathsf{trivial}$ $0.036077686$ $4.305972120$ 3.288129422 \( \frac{399175}{1408} a + \frac{5454499}{1408} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( a + 1\) , \( -a + 3\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+1\right){x}-a+3$
5324.6-d1 5324.6-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/4\Z$ $0.245619348$ $0.288454494$ 3.427684460 \( -\frac{31504873455125}{519691042816} a + \frac{132554493440375}{519691042816} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -48 a - 272\) , \( -3251 a + 4009\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-48a-272\right){x}-3251a+4009$
5324.6-d2 5324.6-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z$ $1.964954788$ $0.288454494$ 3.427684460 \( \frac{31504873455125}{519691042816} a + \frac{50524809992625}{259845521408} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -158 a + 297\) , \( -3796 a + 3141\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-158a+297\right){x}-3796a+3141$
5324.6-d3 5324.6-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.982477394$ $0.288454494$ 3.427684460 \( -\frac{1133731711875}{959512576} a + \frac{4028870229625}{479756288} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -307 a - 542\) , \( -4407 a - 3414\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-307a-542\right){x}-4407a-3414$
5324.6-d4 5324.6-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.491238697$ $0.288454494$ 3.427684460 \( \frac{1133731711875}{959512576} a + \frac{6924008747375}{959512576} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -538 a + 647\) , \( -193 a + 7937\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-538a+647\right){x}-193a+7937$
5324.6-d5 5324.6-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z$ $1.964954788$ $0.144227247$ 3.427684460 \( -\frac{915988506230265125}{54875873536} a + \frac{1519749586080622375}{27437936768} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -4707 a - 8462\) , \( -291111 a - 234502\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-4707a-8462\right){x}-291111a-234502$
5324.6-d6 5324.6-d \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $1$ $\Z/2\Z$ $0.982477394$ $0.144227247$ 3.427684460 \( \frac{915988506230265125}{54875873536} a + \frac{2123510665930979625}{54875873536} \) \( \bigl[1\) , \( 0\) , \( a\) , \( -8298 a + 10087\) , \( -17537 a + 545409\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-8298a+10087\right){x}-17537a+545409$
5324.6-e1 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( -\frac{46830231}{234256} a + \frac{212077575}{117128} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -40 a + 50\) , \( 45 a - 83\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-40a+50\right){x}+45a-83$
5324.6-e2 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( \frac{46830231}{234256} a + \frac{377324919}{234256} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -22 a - 43\) , \( 58 a - 9\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-22a-43\right){x}+58a-9$
5324.6-e3 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.440785834$ 2.665622171 \( -\frac{56046918875913}{857435524} a + \frac{93327675428637}{857435524} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -132 a - 483\) , \( -1724 a - 3749\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-132a-483\right){x}-1724a-3749$
5324.6-e4 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.440785834$ 2.665622171 \( \frac{56046918875913}{857435524} a + \frac{9320189138181}{214358881} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -330 a + 540\) , \( 1213 a + 4369\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-330a+540\right){x}+1213a+4369$
5324.6-e5 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( -\frac{14003310699}{30976} a + \frac{9620888049}{15488} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -76 a - 127\) , \( -548 a - 387\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-76a-127\right){x}-548a-387$
5324.6-e6 5324.6-e \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 11^{3} \) $0$ $\Z/2\Z$ $1$ $0.881571669$ 2.665622171 \( \frac{14003310699}{30976} a + \frac{5238465399}{30976} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -130 a + 152\) , \( -27 a + 1015\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-130a+152\right){x}-27a+1015$
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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.