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Results (22 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
71148.2-a1 71148.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.430413517$ $1.737990332$ 3.455115885 \( \frac{9938375}{274428} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 5 a - 6\) , \( -28\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(5a-6\right){x}-28$
71148.2-a2 71148.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.860827034$ $0.868995166$ 3.455115885 \( \frac{129938649625}{7072758} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -105 a + 104\) , \( -336\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-105a+104\right){x}-336$
71148.2-b1 71148.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.544074716$ $0.068658501$ 3.450739881 \( -\frac{333345918055753}{72923718045024} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -1444 a + 1443\) , \( 412244\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-1444a+1443\right){x}+412244$
71148.2-b2 71148.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.544074716$ $0.274634007$ 3.450739881 \( \frac{29609739866953}{15259926528} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -644 a + 643\) , \( -1708\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-644a+643\right){x}-1708$
71148.2-b3 71148.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.088149433$ $0.137317003$ 3.450739881 \( \frac{21184262604460873}{216872764416} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -5764 a + 5763\) , \( 170324\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-5764a+5763\right){x}+170324$
71148.2-b4 71148.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.176298867$ $0.068658501$ 3.450739881 \( \frac{86129359107301290313}{9166294368} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -92004 a + 92003\) , \( 10795092\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-92004a+92003\right){x}+10795092$
71148.2-c1 71148.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.039411059$ $0.316157574$ 3.625697902 \( -\frac{7347774183121}{6119866368} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -404 a + 404\) , \( 5136\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-404a+404\right){x}+5136$
71148.2-c2 71148.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.078822119$ $0.158078787$ 3.625697902 \( \frac{45637459887836881}{13417633152} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -7444 a + 7444\) , \( 251536\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-7444a+7444\right){x}+251536$
71148.2-d1 71148.2-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.251702057$ $3.507744261$ 4.077970209 \( \frac{4657463}{3696} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 4 a - 5\) , \( -4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(4a-5\right){x}-4$
71148.2-d2 71148.2-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.503404115$ $1.753872130$ 4.077970209 \( \frac{498677257}{213444} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -16 a + 15\) , \( -4\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-16a+15\right){x}-4$
71148.2-d3 71148.2-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.251702057$ $0.876936065$ 4.077970209 \( \frac{223980311017}{4278582} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -126 a + 125\) , \( 612\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-126a+125\right){x}+612$
71148.2-d4 71148.2-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.006808231$ $0.876936065$ 4.077970209 \( \frac{1285429208617}{614922} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -226 a + 225\) , \( -1180\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-226a+225\right){x}-1180$
71148.2-e1 71148.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.464791575$ 2.146780332 \( -\frac{100999381393}{723148272} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -97 a + 97\) , \( 1337\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-97a+97\right){x}+1337$
71148.2-e2 71148.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.116197893$ 2.146780332 \( \frac{4770223741048753}{2740574865798} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3507 a + 3507\) , \( 6507\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-3507a+3507\right){x}+6507$
71148.2-e3 71148.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.232395787$ 2.146780332 \( \frac{1763535241378513}{4612311396} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2517 a + 2517\) , \( 48285\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-2517a+2517\right){x}+48285$
71148.2-e4 71148.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.116197893$ 2.146780332 \( \frac{7209828390823479793}{49509306} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -40247 a + 40247\) , \( 3104415\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-40247a+40247\right){x}+3104415$
71148.2-f1 71148.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.029755661$ 3.573323326 \( -\frac{520203426765625}{11054534935707648} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 1675 a\) , \( 5058506\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+1675a{x}+5058506$
71148.2-f2 71148.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.014877830$ 3.573323326 \( \frac{10228636028672744397625}{167006381634183168} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 452235 a\) , \( 115355594\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+452235a{x}+115355594$
71148.2-g1 71148.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.249083709$ 3.451405122 \( -\frac{61653281712625}{21875235228} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -823 a + 823\) , \( -11611\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-823a+823\right){x}-11611$
71148.2-g2 71148.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.747251128$ 3.451405122 \( \frac{50447927375}{39517632} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 77 a - 77\) , \( 161\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(77a-77\right){x}+161$
71148.2-g3 71148.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.373625564$ 3.451405122 \( \frac{5290763640625}{2291573592} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -363 a + 363\) , \( 1305\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-363a+363\right){x}+1305$
71148.2-g4 71148.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{2} \cdot 11^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.124541854$ 3.451405122 \( \frac{312196988566716625}{25367712678} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -14133 a + 14133\) , \( -647829\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-14133a+14133\right){x}-647829$
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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.