Learn more

Refine search


Results (23 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
14112.5-a1 14112.5-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.420862494$ $1.191573554$ 2.559669408 \( -\frac{519158333}{589824} a + \frac{5078268685}{1769472} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 27 a - 13\) , \( 24 a + 16\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(27a-13\right){x}+24a+16$
14112.5-a2 14112.5-a \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.710431247$ $1.191573554$ 2.559669408 \( \frac{1076146307}{62208} a + \frac{2036360269}{186624} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 17 a + 49\) , \( -78 a + 145\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(17a+49\right){x}-78a+145$
14112.5-b1 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.517880747$ 1.565924189 \( \frac{12134104351}{1376256} a - \frac{12253997573}{1376256} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 189 a + 10\) , \( 364 a + 1336\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(189a+10\right){x}+364a+1336$
14112.5-b2 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.517880747$ 1.565924189 \( -\frac{7189057}{16128} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 83 a - 28\) , \( 438 a + 584\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(83a-28\right){x}+438a+584$
14112.5-b3 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.517880747$ 1.565924189 \( -\frac{12134104351}{1376256} a - \frac{59946611}{688128} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 202 a - 142\) , \( 1070 a + 534\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(202a-142\right){x}+1070a+534$
14112.5-b4 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.064735093$ 1.565924189 \( \frac{6359387729183}{4218578658} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -8107 a + 2702\) , \( 69654 a + 105416\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-8107a+2702\right){x}+69654a+105416$
14112.5-b5 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.129470186$ 1.565924189 \( \frac{124475734657}{63011844} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2183 a - 728\) , \( 9286 a + 12120\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(2183a-728\right){x}+9286a+12120$
14112.5-b6 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.064735093$ 1.565924189 \( \frac{84448510979617}{933897762} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 19193 a - 6398\) , \( -662042 a - 967656\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(19193a-6398\right){x}-662042a-967656$
14112.5-b7 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.258940373$ 1.565924189 \( \frac{65597103937}{63504} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1763 a - 588\) , \( 18806 a + 26120\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(1763a-588\right){x}+18806a+26120$
14112.5-b8 14112.5-b \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.129470186$ 1.565924189 \( \frac{268498407453697}{252} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 28223 a - 9408\) , \( 1197158 a + 1712504\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(28223a-9408\right){x}+1197158a+1712504$
14112.5-c1 14112.5-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.144416270$ 1.528358148 \( -\frac{6329617441}{279936} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 2961 a - 987\) , \( 41391 a + 59787\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(2961a-987\right){x}+41391a+59787$
14112.5-c2 14112.5-c \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.010913893$ 1.528358148 \( -\frac{2401}{6} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 21 a - 7\) , \( -63 a - 91\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(21a-7\right){x}-63a-91$
14112.5-d1 14112.5-d \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.036107404$ $2.054306579$ 5.831440488 \( -\frac{1334593}{8192} a + \frac{51008081}{24576} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -2 a + 11\) , \( a + 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+11\right){x}+a+3$
14112.5-e1 14112.5-e \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.799329299$ $0.499124703$ 6.031783824 \( \frac{446668992275}{2016} a - \frac{316677731777}{2016} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 103 a - 1300\) , \( -2073 a + 18533\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(103a-1300\right){x}-2073a+18533$
14112.5-e2 14112.5-e \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.399664649$ $0.499124703$ 6.031783824 \( -\frac{5744242075}{580608} a - \frac{3197221351}{580608} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -229 a + 44\) , \( -1679 a + 1907\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-229a+44\right){x}-1679a+1907$
14112.5-e3 14112.5-e \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.199832324$ $0.499124703$ 6.031783824 \( \frac{100686965405}{66060288} a - \frac{34122302927}{66060288} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 63 a + 139\) , \( 539 a - 1273\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(63a+139\right){x}+539a-1273$
14112.5-e4 14112.5-e \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.799329299$ $0.249562351$ 6.031783824 \( -\frac{218546645}{1143072} a - \frac{3116347217}{10287648} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 51 a - 516\) , \( -3079 a + 9411\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(51a-516\right){x}-3079a+9411$
14112.5-f1 14112.5-f \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.639934178$ 3.869958154 \( -\frac{125632169}{196} a - \frac{31841287}{12} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3 a - 447\) , \( 75 a + 3675\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-3a-447\right){x}+75a+3675$
14112.5-f2 14112.5-f \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.279868357$ 3.869958154 \( \frac{14150117}{756} a - \frac{42134837}{2268} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 23 a - 52\) , \( -111 a + 135\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(23a-52\right){x}-111a+135$
14112.5-f3 14112.5-f \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $1.279868357$ 3.869958154 \( \frac{2117957}{1792} a + \frac{1884523}{5376} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 18 a - 25\) , \( -39 a + 43\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(18a-25\right){x}-39a+43$
14112.5-f4 14112.5-f \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.279868357$ 3.869958154 \( -\frac{413801}{336} a + \frac{1624825}{1008} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -3 a - 27\) , \( -9 a + 63\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(-3a-27\right){x}-9a+63$
14112.5-g1 14112.5-g \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.126591401$ $0.541165759$ 6.214364745 \( -\frac{16591834777}{98304} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 305 a - 102\) , \( 1374 a + 1804\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(305a-102\right){x}+1374a+1804$
14112.5-g2 14112.5-g \(\Q(\sqrt{-7}) \) \( 2^{5} \cdot 3^{2} \cdot 7^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.042197133$ $1.623497278$ 6.214364745 \( \frac{596183}{864} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -10 a + 3\) , \( 9 a + 19\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-10a+3\right){x}+9a+19$
  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.