Learn more

Refine search


Results (16 matches)

  Download to        
Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
56.1-a1 56.1-a \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $22.75712104$ 3.041048216 \( -\frac{4}{7} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 4\) , \( 2\bigr] \) ${y}^2+a{x}{y}={x}^{3}+4{x}+2$
56.1-a2 56.1-a \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $22.75712104$ 3.041048216 \( \frac{3543122}{49} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -6\) , \( 2\bigr] \) ${y}^2+a{x}{y}={x}^{3}-6{x}+2$
56.1-b1 56.1-b \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/2\Z$ $3.866114466$ $12.23735606$ 3.161100443 \( -\frac{39775849362076815}{7} a + 21261085797246696 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -8820 a - 33003\) , \( 912600 a + 3414635\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-8820a-33003\right){x}+912600a+3414635$
56.1-b2 56.1-b \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/4\Z$ $1.933057233$ $24.47471212$ 3.161100443 \( \frac{432}{7} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -30 a + 112\) , \( -944 a + 3532\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-30a+112\right){x}-944a+3532$
56.1-b3 56.1-b \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/2\Z$ $1.933057233$ $6.118678030$ 3.161100443 \( \frac{11090466}{2401} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 1770 a - 6623\) , \( 64686 a - 242033\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1770a-6623\right){x}+64686a-242033$
56.1-b4 56.1-b \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.966528616$ $24.47471212$ 3.161100443 \( \frac{740772}{49} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -570 a - 2133\) , \( 12630 a + 47257\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-570a-2133\right){x}+12630a+47257$
56.1-b5 56.1-b \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.933057233$ $24.47471212$ 3.161100443 \( \frac{1443468546}{7} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 8970 a - 33563\) , \( -881050 a + 3296587\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(8970a-33563\right){x}-881050a+3296587$
56.1-b6 56.1-b \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/2\Z$ $3.866114466$ $12.23735606$ 3.161100443 \( \frac{39775849362076815}{7} a + 21261085797246696 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 8820 a - 33003\) , \( -912600 a + 3414635\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(8820a-33003\right){x}-912600a+3414635$
56.1-c1 56.1-c \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/2\Z$ $0.844493815$ $7.189921948$ 1.622768733 \( -\frac{4}{7} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 7 a - 33\) , \( 1856 a - 6948\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-33\right){x}+1856a-6948$
56.1-c2 56.1-c \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $1$ $\Z/2\Z$ $0.422246907$ $7.189921948$ 1.622768733 \( \frac{3543122}{49} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 1207 a - 4523\) , \( 47106 a - 176258\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1207a-4523\right){x}+47106a-176258$
56.1-d1 56.1-d \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $2$ $\Z/2\Z$ $32.36335355$ $0.659073382$ 2.850317744 \( -\frac{39775849362076815}{7} a + 21261085797246696 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 150 a - 635\) , \( 2318 a - 9041\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(150a-635\right){x}+2318a-9041$
56.1-d2 56.1-d \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $2$ $\Z/4\Z$ $2.022709596$ $10.54517411$ 2.850317744 \( \frac{432}{7} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
56.1-d3 56.1-d \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $2$ $\Z/4\Z$ $0.505677399$ $10.54517411$ 2.850317744 \( \frac{11090466}{2401} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -15\) , \( -5\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-15{x}-5$
56.1-d4 56.1-d \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $2$ $\Z/2\Z\oplus\Z/4\Z$ $2.022709596$ $10.54517411$ 2.850317744 \( \frac{740772}{49} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -11\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-5{x}-11$
56.1-d5 56.1-d \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $8.090838387$ $2.636293528$ 2.850317744 \( \frac{1443468546}{7} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -75\) , \( -361\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-75{x}-361$
56.1-d6 56.1-d \(\Q(\sqrt{14}) \) \( 2^{3} \cdot 7 \) $2$ $\Z/2\Z$ $32.36335355$ $0.659073382$ 2.850317744 \( \frac{39775849362076815}{7} a + 21261085797246696 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -150 a - 635\) , \( -2318 a - 9041\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-150a-635\right){x}-2318a-9041$
  Download to        

  *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.