Learn more

Refine search


Results (16 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
1568.2-a1 1568.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.168455059$ $3.319686739$ 1.690916372 \( -\frac{16471}{4} a + \frac{2971}{4} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -4 a + 5\) , \( a + 4\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-4a+5\right){x}+a+4$
1568.2-a2 1568.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.084227529$ $3.319686739$ 1.690916372 \( \frac{16471}{4} a - 3375 \) \( \bigl[a\) , \( a\) , \( 0\) , \( -4 a\) , \( -4 a + 8\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}-4a{x}-4a+8$
1568.2-a3 1568.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.179185414$ $0.474240962$ 1.690916372 \( -\frac{1875341}{16384} a + \frac{29156511}{16384} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 116 a + 85\) , \( 191 a - 336\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(116a+85\right){x}+191a-336$
1568.2-a4 1568.2-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.589592707$ $0.474240962$ 1.690916372 \( \frac{1875341}{16384} a + \frac{13640585}{8192} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 86 a - 220\) , \( -44 a - 392\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(86a-220\right){x}-44a-392$
1568.2-b1 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.165438288$ 2.251072633 \( -\frac{548347731625}{1835008} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -3581 a + 2388\) , \( 55046 a - 134557\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-3581a+2388\right){x}+55046a-134557$
1568.2-b2 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.496314864$ 2.251072633 \( -\frac{10538337875}{200704} a - \frac{13018580375}{100352} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 269 a + 194\) , \( 1017 a - 4482\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(269a+194\right){x}+1017a-4482$
1568.2-b3 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.496314864$ 2.251072633 \( \frac{10538337875}{200704} a - \frac{36575498625}{200704} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 200 a - 507\) , \( 2267 a - 4120\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(200a-507\right){x}+2267a-4120$
1568.2-b4 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.488944592$ 2.251072633 \( -\frac{831875}{112} a - \frac{166375}{112} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 25 a - 17\) , \( -36 a - 46\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-17\right){x}-36a-46$
1568.2-b5 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.488944592$ 2.251072633 \( \frac{831875}{112} a - \frac{499125}{56} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 24 a - 16\) , \( 44 a + 12\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(24a-16\right){x}+44a+12$
1568.2-b6 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.488944592$ 2.251072633 \( -\frac{15625}{28} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -11 a + 8\) , \( -16 a + 39\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-11a+8\right){x}-16a+39$
1568.2-b7 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.496314864$ 2.251072633 \( \frac{9938375}{21952} \) \( \bigl[a\) , \( -a\) , \( a\) , \( 94 a - 62\) , \( 362 a - 885\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(94a-62\right){x}+362a-885$
1568.2-b8 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.165438288$ 2.251072633 \( -\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -606 a - 716\) , \( 5616 a - 23564\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-606a-716\right){x}+5616a-23564$
1568.2-b9 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.165438288$ 2.251072633 \( \frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -395 a + 1383\) , \( 13026 a - 20402\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-395a+1383\right){x}+13026a-20402$
1568.2-b10 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.248157432$ 2.251072633 \( \frac{4956477625}{941192} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -746 a + 498\) , \( 4394 a - 10741\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-746a+498\right){x}+4394a-10741$
1568.2-b11 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.744472296$ 2.251072633 \( \frac{128787625}{98} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -221 a + 148\) , \( -772 a + 1887\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-221a+148\right){x}-772a+1887$
1568.2-b12 1568.2-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.082719144$ 2.251072633 \( \frac{2251439055699625}{25088} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -57341 a + 38228\) , \( 3474182 a - 8492445\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-57341a+38228\right){x}+3474182a-8492445$
  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.