Learn more

Refine search


Results (8 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
81.4-a1 81.4-a \(\Q(\sqrt{13}) \) \( 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.586269779$ 1.549352471 \( -3874871 a - 5047588 \) \( \bigl[a\) , \( -1\) , \( a + 1\) , \( -7 a + 12\) , \( -16 a + 34\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-7a+12\right){x}-16a+34$
81.4-a2 81.4-a \(\Q(\sqrt{13}) \) \( 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.586269779$ 1.549352471 \( 175 a - 403 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 2 a + 2\) , \( a + 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$
81.4-b1 81.4-b \(\Q(\sqrt{13}) \) \( 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $5.274169784$ 1.462791507 \( -7081984 a + 16347136 \) \( \bigl[0\) , \( -a + 1\) , \( a\) , \( 20 a - 50\) , \( 89 a - 208\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(20a-50\right){x}+89a-208$
81.4-b2 81.4-b \(\Q(\sqrt{13}) \) \( 3^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $47.46752806$ 1.462791507 \( 20480 a + 28672 \) \( \bigl[0\) , \( -a + 1\) , \( a\) , \( 0\) , \( -1\bigr] \) ${y}^2+a{y}={x}^{3}+\left(-a+1\right){x}^{2}-1$
81.4-c1 81.4-c \(\Q(\sqrt{13}) \) \( 3^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.073680404$ $24.79923923$ 1.013558173 \( -7081984 a + 16347136 \) \( \bigl[0\) , \( a - 1\) , \( a\) , \( 3 a - 9\) , \( -10 a + 19\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(3a-9\right){x}-10a+19$
81.4-c2 81.4-c \(\Q(\sqrt{13}) \) \( 3^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.024560134$ $24.79923923$ 1.013558173 \( 20480 a + 28672 \) \( \bigl[0\) , \( a - 1\) , \( a\) , \( 2 a - 5\) , \( -a + 1\bigr] \) ${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-5\right){x}-a+1$
81.4-d1 81.4-d \(\Q(\sqrt{13}) \) \( 3^{4} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $2.434315372$ 0.675157607 \( -3874871 a - 5047588 \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( -19 a - 24\) , \( -94 a - 123\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-19a-24\right){x}-94a-123$
81.4-d2 81.4-d \(\Q(\sqrt{13}) \) \( 3^{4} \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $21.90883835$ 0.675157607 \( 175 a - 403 \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( a + 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a+1\right){x}$
  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.