Learn more

Refine search


Results (22 matches)

  displayed columns for results
Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
28812.3-a1 28812.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.109168439$ 1.764795976 \( -\frac{6329617441}{279936} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 6909 a\) , \( -232261\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+6909a{x}-232261$
28812.3-a2 28812.3-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.764179074$ 1.764795976 \( -\frac{2401}{6} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 49 a\) , \( 293\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+49a{x}+293$
28812.3-b1 28812.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.058440408$ 2.024435147 \( -\frac{16591834777}{98304} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -34864 a + 34863\) , \( 2538800\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-34864a+34863\right){x}+2538800$
28812.3-b2 28812.3-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.175321226$ 2.024435147 \( \frac{596183}{864} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 1151 a - 1152\) , \( 17750\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(1151a-1152\right){x}+17750$
28812.3-c1 28812.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.229529190$ 2.120299834 \( \frac{4913}{1296} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 122\) , \( -10940\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+122{x}-10940$
28812.3-c2 28812.3-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.114764595$ 2.120299834 \( \frac{838561807}{26244} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -6738\) , \( -209880\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-6738{x}-209880$
28812.3-d1 28812.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.245324381$ 2.266209564 \( \frac{28037148049}{2117682} a - \frac{2552218955}{117649} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -1109 a - 351\) , \( -21852 a + 4784\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1109a-351\right){x}-21852a+4784$
28812.3-d2 28812.3-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.490648763$ 2.266209564 \( \frac{2016793}{4116} a - \frac{2483137}{4116} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -129 a + 139\) , \( -586 a - 704\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-129a+139\right){x}-586a-704$
28812.3-e1 28812.3-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.245324381$ 2.266209564 \( -\frac{28037148049}{2117682} a - \frac{17902793141}{2117682} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -1461 a + 352\) , \( 21851 a - 17068\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-1461a+352\right){x}+21851a-17068$
28812.3-e2 28812.3-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.490648763$ 2.266209564 \( -\frac{2016793}{4116} a - \frac{38862}{343} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 9 a - 138\) , \( 585 a - 1290\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(9a-138\right){x}+585a-1290$
28812.3-f1 28812.3-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.138307751$ $0.391481047$ 4.001350588 \( -\frac{7189057}{16128} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -197 a + 197\) , \( -2367\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-197a+197\right){x}-2367$
28812.3-f2 28812.3-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.106462011$ $0.048935130$ 4.001350588 \( \frac{6359387729183}{4218578658} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 18913 a - 18913\) , \( -381333\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(18913a-18913\right){x}-381333$
28812.3-f3 28812.3-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.553231005$ $0.097870261$ 4.001350588 \( \frac{124475734657}{63011844} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -5097 a + 5097\) , \( -49995\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-5097a+5097\right){x}-49995$
28812.3-f4 28812.3-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.106462011$ $0.048935130$ 4.001350588 \( \frac{84448510979617}{933897762} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -44787 a + 44787\) , \( 3609423\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-44787a+44787\right){x}+3609423$
28812.3-f5 28812.3-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.276615502$ $0.195740523$ 4.001350588 \( \frac{65597103937}{63504} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -4117 a + 4117\) , \( -101935\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-4117a+4117\right){x}-101935$
28812.3-f6 28812.3-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.553231005$ $0.097870261$ 4.001350588 \( \frac{268498407453697}{252} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -65857 a + 65857\) , \( -6510547\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-65857a+65857\right){x}-6510547$
28812.3-g1 28812.3-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.141160516$ $0.409082862$ 4.000784346 \( -\frac{16591834777}{98304} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 711 a\) , \( -7402\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+711a{x}-7402$
28812.3-g2 28812.3-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.047053505$ $1.227248586$ 4.000784346 \( \frac{596183}{864} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( -24 a\) , \( -52\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-24a{x}-52$
28812.3-h1 28812.3-h \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.033626968$ $1.606704330$ 3.992758292 \( \frac{4913}{1296} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 2\) , \( 32\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+2{x}+32$
28812.3-h2 28812.3-h \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.067253936$ $0.803352165$ 3.992758292 \( \frac{838561807}{26244} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -138\) , \( 592\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-138{x}+592$
28812.3-i1 28812.3-i \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\Z/7\Z$ $\mathrm{SU}(2)$ $1.160660403$ $0.764179074$ 4.096657620 \( -\frac{6329617441}{279936} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 141 a\) , \( 657\bigr] \) ${y}^2+a{x}{y}={x}^{3}+141a{x}+657$
28812.3-i2 28812.3-i \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 7^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.165808629$ $5.349253519$ 4.096657620 \( -\frac{2401}{6} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( a\) , \( -1\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}-1$
  displayed columns for results

  *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.