Learn more

Refine search


Results (20 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
3969.1-a1 3969.1-a \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $5.120490302$ 1.810366707 \( -\frac{551719468601289472}{49} a + \frac{780249146376863552}{49} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 3514 a - 8283\) , \( -179933 a + 326221\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(3514a-8283\right){x}-179933a+326221$
3969.1-a2 3969.1-a \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $5.120490302$ 1.810366707 \( -\frac{13219923200}{117649} a + \frac{18683377472}{117649} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 49 a - 93\) , \( -194 a + 448\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(49a-93\right){x}-194a+448$
3969.1-a3 3969.1-a \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.120490302$ 1.810366707 \( -\frac{210688}{49} a + \frac{302912}{49} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 4 a - 3\) , \( 4 a - 11\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(4a-3\right){x}+4a-11$
3969.1-a4 3969.1-a \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.120490302$ 1.810366707 \( \frac{210688}{49} a + \frac{302912}{49} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -5 a - 3\) , \( -4 a - 11\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-5a-3\right){x}-4a-11$
3969.1-a5 3969.1-a \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $5.120490302$ 1.810366707 \( \frac{13219923200}{117649} a + \frac{18683377472}{117649} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -50 a - 93\) , \( 194 a + 448\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-50a-93\right){x}+194a+448$
3969.1-a6 3969.1-a \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $5.120490302$ 1.810366707 \( \frac{551719468601289472}{49} a + \frac{780249146376863552}{49} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -3515 a - 8283\) , \( 179933 a + 326221\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-3515a-8283\right){x}+179933a+326221$
3969.1-b1 3969.1-b \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.217293980$ 1.721513656 \( -\frac{4354703137}{17294403} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -306\) , \( 5859\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-306{x}+5859$
3969.1-b2 3969.1-b \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.869175922$ 1.721513656 \( \frac{103823}{63} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$
3969.1-b3 3969.1-b \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.869175922$ 1.721513656 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -36\) , \( 27\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-36{x}+27$
3969.1-b4 3969.1-b \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.217293980$ 1.721513656 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -351\) , \( -2430\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-351{x}-2430$
3969.1-b5 3969.1-b \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.869175922$ 1.721513656 \( \frac{13027640977}{21609} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -441\) , \( 3672\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-441{x}+3672$
3969.1-b6 3969.1-b \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $4.869175922$ 1.721513656 \( \frac{53297461115137}{147} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -7056\) , \( 229905\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-7056{x}+229905$
3969.1-c1 3969.1-c \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.350443682$ 1.432361828 \( -\frac{211597056}{117649} a - \frac{25299648}{117649} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 148 a - 223\) , \( 688 a - 1003\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(148a-223\right){x}+688a-1003$
3969.1-c2 3969.1-c \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $12.15399314$ 1.432361828 \( -\frac{1441034496}{343} a + \frac{2038364352}{343} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 16 a + 17\) , \( 27 a + 41\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(16a+17\right){x}+27a+41$
3969.1-c3 3969.1-c \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $12.15399314$ 1.432361828 \( \frac{211597056}{117649} a - \frac{25299648}{117649} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -17 a - 25\) , \( 14 a + 20\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-17a-25\right){x}+14a+20$
3969.1-c4 3969.1-c \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.350443682$ 1.432361828 \( \frac{1441034496}{343} a + \frac{2038364352}{343} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -149 a + 155\) , \( 445 a - 814\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-149a+155\right){x}+445a-814$
3969.1-d1 3969.1-d \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $12.15399314$ 1.432361828 \( -\frac{211597056}{117649} a - \frac{25299648}{117649} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 16 a - 25\) , \( -15 a + 20\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(16a-25\right){x}-15a+20$
3969.1-d2 3969.1-d \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.350443682$ 1.432361828 \( -\frac{1441034496}{343} a + \frac{2038364352}{343} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 148 a + 155\) , \( -446 a - 814\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(148a+155\right){x}-446a-814$
3969.1-d3 3969.1-d \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.350443682$ 1.432361828 \( \frac{211597056}{117649} a - \frac{25299648}{117649} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -149 a - 223\) , \( -689 a - 1003\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-149a-223\right){x}-689a-1003$
3969.1-d4 3969.1-d \(\Q(\sqrt{2}) \) \( 3^{4} \cdot 7^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $12.15399314$ 1.432361828 \( \frac{1441034496}{343} a + \frac{2038364352}{343} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -17 a + 17\) , \( -28 a + 41\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-17a+17\right){x}-28a+41$
  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.