Learn more

Refine search


Results (24 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
2500.3-a1 2500.3-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.284833349$ 0.515282916 \( -\frac{349938025}{8} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3138{x}-68969$
2500.3-a2 2500.3-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $4.272500240$ 0.515282916 \( -\frac{121945}{32} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-3{x}+1$
2500.3-a3 2500.3-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.854500048$ 0.515282916 \( -\frac{25}{2} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( -219\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-13{x}-219$
2500.3-a4 2500.3-a \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\Z/5\Z$ $\mathrm{SU}(2)$ $1$ $1.424166746$ 0.515282916 \( \frac{46969655}{32768} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+22{x}-9$
2500.3-b1 2500.3-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.636906731$ 1.152207629 \( -\frac{349938025}{8} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 376 a - 126\) , \( 2207 a + 3862\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(376a-126\right){x}+2207a+3862$
2500.3-b2 2500.3-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.910720194$ 1.152207629 \( -\frac{121945}{32} \) \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( -11 a + 7\) , \( 13 a - 18\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-11a+7\right){x}+13a-18$
2500.3-b3 2500.3-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.910720194$ 1.152207629 \( -\frac{25}{2} \) \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( a - 1\) , \( 7 a + 12\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-1\right){x}+7a+12$
2500.3-b4 2500.3-b \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.636906731$ 1.152207629 \( \frac{46969655}{32768} \) \( \bigl[a\) , \( a - 1\) , \( a + 1\) , \( 64 a - 43\) , \( -102 a + 142\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(64a-43\right){x}-102a+142$
2500.3-c1 2500.3-c \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.187131889$ $1.873441976$ 3.382530227 \( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -7 a + 6\) , \( -12 a + 13\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-7a+6\right){x}-12a+13$
2500.3-c2 2500.3-c \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.037426377$ $1.873441976$ 3.382530227 \( -\frac{344373}{160} a + \frac{580523}{80} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -10 a - 7\) , \( 15 a + 14\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-10a-7\right){x}+15a+14$
2500.3-d1 2500.3-d \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.636906731$ 1.152207629 \( -\frac{349938025}{8} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -377 a + 251\) , \( -2207 a + 6069\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-377a+251\right){x}-2207a+6069$
2500.3-d2 2500.3-d \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.910720194$ 1.152207629 \( -\frac{121945}{32} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 8 a - 5\) , \( -9 a - 32\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(8a-5\right){x}-9a-32$
2500.3-d3 2500.3-d \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.910720194$ 1.152207629 \( -\frac{25}{2} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -2 a + 1\) , \( -7 a + 19\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-2a+1\right){x}-7a+19$
2500.3-d4 2500.3-d \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.636906731$ 1.152207629 \( \frac{46969655}{32768} \) \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -67 a + 20\) , \( 56 a + 238\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-67a+20\right){x}+56a+238$
2500.3-e1 2500.3-e \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.187131889$ $1.873441976$ 3.382530227 \( \frac{2632683}{6250} a - \frac{535861}{3125} \) \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 5 a\) , \( 11 a + 1\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+5a{x}+11a+1$
2500.3-e2 2500.3-e \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.037426377$ $1.873441976$ 3.382530227 \( \frac{344373}{160} a + \frac{816673}{160} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 9 a - 19\) , \( -22 a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(9a-19\right){x}-22a+1$
2500.3-f1 2500.3-f \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.837828722$ 2.020918916 \( \frac{2632683}{6250} a - \frac{535861}{3125} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -50\) , \( -81 a - 146\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-50{x}-81a-146$
2500.3-f2 2500.3-f \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.837828722$ 2.020918916 \( \frac{344373}{160} a + \frac{816673}{160} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -38 a - 51\) , \( 168 a + 30\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-38a-51\right){x}+168a+30$
2500.3-g1 2500.3-g \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.837828722$ 2.020918916 \( -\frac{2632683}{6250} a + \frac{1560961}{6250} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a - 48\) , \( 80 a - 226\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a-48\right){x}+80a-226$
2500.3-g2 2500.3-g \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.837828722$ 2.020918916 \( -\frac{344373}{160} a + \frac{580523}{80} \) \( \bigl[1\) , \( 0\) , \( a\) , \( 37 a - 88\) , \( -169 a + 199\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(37a-88\right){x}-169a+199$
2500.3-h1 2500.3-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $1.424166746$ 2.576414584 \( -\frac{349938025}{8} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-126{x}-552$
2500.3-h2 2500.3-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $0.854500048$ 2.576414584 \( -\frac{121945}{32} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-76{x}+298$
2500.3-h3 2500.3-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $4.272500240$ 2.576414584 \( -\frac{25}{2} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}-2$
2500.3-h4 2500.3-h \(\Q(\sqrt{-11}) \) \( 2^{2} \cdot 5^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.284833349$ 2.576414584 \( \frac{46969655}{32768} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+549{x}-2202$
  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.