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Results (32 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
350.1-a1 350.1-a \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $5.572473402$ 2.106196972 \( \frac{1367631}{2800} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+2{x}-3$
350.1-a2 350.1-a \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.572473402$ 2.106196972 \( \frac{611960049}{122500} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -18\) , \( -19\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-18{x}-19$
350.1-a3 350.1-a \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $5.572473402$ 2.106196972 \( \frac{74565301329}{5468750} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -88\) , \( 317\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-88{x}+317$
350.1-a4 350.1-a \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.393118350$ 2.106196972 \( \frac{2121328796049}{120050} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -268\) , \( -1619\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-268{x}-1619$
350.1-b1 350.1-b \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.195941934$ 4.079715601 \( -\frac{1063801}{140} a + \frac{6446741}{320} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 129 a - 339\) , \( 1164 a - 3079\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(129a-339\right){x}+1164a-3079$
350.1-b2 350.1-b \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.597970967$ 4.079715601 \( -\frac{51602522987}{175} a + \frac{1092243955769}{1400} \) \( \bigl[a\) , \( a\) , \( a\) , \( -1836 a - 4861\) , \( -68869 a - 182212\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-1836a-4861\right){x}-68869a-182212$
350.1-c1 350.1-c \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.262897143$ 1.611223672 \( \frac{698819}{14} a - \frac{22823084}{175} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 28 a - 73\) , \( 111 a - 296\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(28a-73\right){x}+111a-296$
350.1-c2 350.1-c \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.262897143$ 1.611223672 \( -\frac{6416115308231}{490} a + \frac{3395089275377}{98} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 453 a - 1198\) , \( 8186 a - 21661\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(453a-1198\right){x}+8186a-21661$
350.1-d1 350.1-d \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.062547888$ 0.401605352 \( \frac{1136672039941}{89600} a - \frac{375900716717}{11200} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 1325 a + 3507\) , \( -8897 a - 23541\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1325a+3507\right){x}-8897a-23541$
350.1-d2 350.1-d \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.062547888$ 0.401605352 \( -\frac{6676332909114256153}{7840} a + \frac{17663916547407093589}{7840} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -5475 a - 14493\) , \( -93377 a - 247061\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-5475a-14493\right){x}-93377a-247061$
350.1-e1 350.1-e \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.262897143$ 1.611223672 \( -\frac{698819}{14} a - \frac{22823084}{175} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -29 a - 73\) , \( -112 a - 296\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-29a-73\right){x}-112a-296$
350.1-e2 350.1-e \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.262897143$ 1.611223672 \( \frac{6416115308231}{490} a + \frac{3395089275377}{98} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -454 a - 1198\) , \( -8187 a - 21661\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-454a-1198\right){x}-8187a-21661$
350.1-f1 350.1-f \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.062547888$ 0.401605352 \( -\frac{1136672039941}{89600} a - \frac{375900716717}{11200} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1326 a + 3507\) , \( 8897 a - 23541\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1326a+3507\right){x}+8897a-23541$
350.1-f2 350.1-f \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.062547888$ 0.401605352 \( \frac{6676332909114256153}{7840} a + \frac{17663916547407093589}{7840} \) \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 5474 a - 14493\) , \( 93377 a - 247061\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(5474a-14493\right){x}+93377a-247061$
350.1-g1 350.1-g \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.195941934$ 4.079715601 \( \frac{1063801}{140} a + \frac{6446741}{320} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( -129 a - 339\) , \( -1164 a - 3079\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-129a-339\right){x}-1164a-3079$
350.1-g2 350.1-g \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.597970967$ 4.079715601 \( \frac{51602522987}{175} a + \frac{1092243955769}{1400} \) \( \bigl[a\) , \( -a\) , \( a\) , \( 1836 a - 4861\) , \( 68869 a - 182212\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(1836a-4861\right){x}+68869a-182212$
350.1-h1 350.1-h \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.148495818$ $18.75601023$ 3.158107589 \( \frac{1063801}{140} a + \frac{6446741}{320} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -127 a - 336\) , \( 1036 a + 2741\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-127a-336\right){x}+1036a+2741$
350.1-h2 350.1-h \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.074247909$ $18.75601023$ 3.158107589 \( \frac{51602522987}{175} a + \frac{1092243955769}{1400} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 1838 a - 4858\) , \( -67032 a + 177352\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(1838a-4858\right){x}-67032a+177352$
350.1-i1 350.1-i \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.668360963$ $6.501685124$ 3.284868475 \( -\frac{1136672039941}{89600} a - \frac{375900716717}{11200} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -1324 a + 3504\) , \( -10222 a + 27044\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-1324a+3504\right){x}-10222a+27044$
350.1-i2 350.1-i \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.336721927$ $6.501685124$ 3.284868475 \( \frac{6676332909114256153}{7840} a + \frac{17663916547407093589}{7840} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( 5476 a - 14496\) , \( -87902 a + 232564\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(5476a-14496\right){x}-87902a+232564$
350.1-j1 350.1-j \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.114097895$ $17.94327116$ 1.547605377 \( -\frac{698819}{14} a - \frac{22823084}{175} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -27 a - 70\) , \( 84 a + 222\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-27a-70\right){x}+84a+222$
350.1-j2 350.1-j \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.228195790$ $17.94327116$ 1.547605377 \( \frac{6416115308231}{490} a + \frac{3395089275377}{98} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -452 a - 1195\) , \( 7734 a + 20462\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-452a-1195\right){x}+7734a+20462$
350.1-k1 350.1-k \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.668360963$ $6.501685124$ 3.284868475 \( \frac{1136672039941}{89600} a - \frac{375900716717}{11200} \) \( \bigl[a\) , \( -a\) , \( a + 1\) , \( 1323 a + 3504\) , \( 10221 a + 27044\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1323a+3504\right){x}+10221a+27044$
350.1-k2 350.1-k \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.336721927$ $6.501685124$ 3.284868475 \( -\frac{6676332909114256153}{7840} a + \frac{17663916547407093589}{7840} \) \( \bigl[a\) , \( -a\) , \( a + 1\) , \( -5477 a - 14496\) , \( 87901 a + 232564\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-5477a-14496\right){x}+87901a+232564$
350.1-l1 350.1-l \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.114097895$ $17.94327116$ 1.547605377 \( \frac{698819}{14} a - \frac{22823084}{175} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 26 a - 70\) , \( -84 a + 222\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(26a-70\right){x}-84a+222$
350.1-l2 350.1-l \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.228195790$ $17.94327116$ 1.547605377 \( -\frac{6416115308231}{490} a + \frac{3395089275377}{98} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 451 a - 1195\) , \( -7734 a + 20462\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(451a-1195\right){x}-7734a+20462$
350.1-m1 350.1-m \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.148495818$ $18.75601023$ 3.158107589 \( -\frac{1063801}{140} a + \frac{6446741}{320} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 127 a - 336\) , \( -1036 a + 2741\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(127a-336\right){x}-1036a+2741$
350.1-m2 350.1-m \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.074247909$ $18.75601023$ 3.158107589 \( -\frac{51602522987}{175} a + \frac{1092243955769}{1400} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -1838 a - 4858\) , \( 67032 a + 177352\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1838a-4858\right){x}+67032a+177352$
350.1-n1 350.1-n \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.613941328$ $9.826603825$ 4.560487736 \( \frac{1367631}{2800} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -1\) , \( 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-{x}+1$
350.1-n2 350.1-n \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.306970664$ $9.826603825$ 4.560487736 \( \frac{611960049}{122500} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -21\) , \( 17\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-21{x}+17$
350.1-n3 350.1-n \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.613941328$ $2.456650956$ 4.560487736 \( \frac{74565301329}{5468750} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -91\) , \( -319\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-91{x}-319$
350.1-n4 350.1-n \(\Q(\sqrt{7}) \) \( 2 \cdot 5^{2} \cdot 7 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.613941328$ $9.826603825$ 4.560487736 \( \frac{2121328796049}{120050} \) \( \bigl[a\) , \( -1\) , \( a\) , \( -271\) , \( 1617\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}-271{x}+1617$
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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.