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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
3.1-a1 3.1-a \(\Q(\sqrt{433}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.382800226$ $33.64129478$ 4.950977218 \( -\frac{897944}{81} a - \frac{8770081}{81} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -50024838009 a + 545487142956\) , \( -7185964954797827 a + 78358104659428531\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-50024838009a+545487142956\right){x}-7185964954797827a+78358104659428531$
3.2-a1 3.2-a \(\Q(\sqrt{433}) \) \( 3 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.382800226$ $33.64129478$ 4.950977218 \( \frac{897944}{81} a - \frac{358075}{3} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 50024838009 a + 495462304947\) , \( 7185964954797827 a + 71172139704630704\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(50024838009a+495462304947\right){x}+7185964954797827a+71172139704630704$
4.1-a1 4.1-a \(\Q(\sqrt{433}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $23.79940653$ 8.006085419 \( \frac{653341}{128} a + \frac{1619595}{32} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -183596225915247433 a + 2001993104035084020\) , \( 738396121317306709527577766 a - 8051712041215403718971174891\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-183596225915247433a+2001993104035084020\right){x}+738396121317306709527577766a-8051712041215403718971174891$
4.1-b1 4.1-b \(\Q(\sqrt{433}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.224585625$ $27.01677809$ 5.248607171 \( -\frac{1041157}{256} a - \frac{9606923}{512} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 3221641116 a - 35129825064\) , \( -307897027602031 a + 3357409570590572\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3221641116a-35129825064\right){x}-307897027602031a+3357409570590572$
4.1-c1 4.1-c \(\Q(\sqrt{433}) \) \( 2^{2} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.224585625$ $27.01677809$ 5.248607171 \( \frac{1041157}{256} a - \frac{11689237}{512} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -3221641117 a - 31908183948\) , \( 307897027602030 a + 3049512542988541\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-3221641117a-31908183948\right){x}+307897027602030a+3049512542988541$
4.1-d1 4.1-d \(\Q(\sqrt{433}) \) \( 2^{2} \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $23.79940653$ 8.006085419 \( -\frac{653341}{128} a + \frac{7131721}{128} \) \( \bigl[1\) , \( -a\) , \( a\) , \( 183596225915247432 a + 1818396878119836588\) , \( -738396121317306709527577767 a - 7313315919898097009443597124\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(183596225915247432a+1818396878119836588\right){x}-738396121317306709527577767a-7313315919898097009443597124$
4.1-e1 4.1-e \(\Q(\sqrt{433}) \) \( 2^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $11.52772170$ $24.53113644$ 1.286620543 \( -\frac{8481}{64} a - \frac{4891}{16} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( -29530642419 a - 292481110197\) , \( 12559811845011234 a + 124396471304828960\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-29530642419a-292481110197\right){x}+12559811845011234a+124396471304828960$
4.1-e2 4.1-e \(\Q(\sqrt{433}) \) \( 2^{2} \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $11.52772170$ $24.53113644$ 1.286620543 \( \frac{8481}{64} a - \frac{28045}{64} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 29530642419 a - 322011752616\) , \( -12559811845011234 a + 136956283149840194\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(29530642419a-322011752616\right){x}-12559811845011234a+136956283149840194$
6.2-a1 6.2-a \(\Q(\sqrt{433}) \) \( 2 \cdot 3 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.170804502$ $13.50686390$ 1.773903022 \( -\frac{3500231839}{331776} a - \frac{1281595783}{12288} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -8433891771 a - 83532013715\) , \( 1365231161498006 a + 13521694520702646\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-8433891771a-83532013715\right){x}+1365231161498006a+13521694520702646$
6.3-a1 6.3-a \(\Q(\sqrt{433}) \) \( 2 \cdot 3 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.170804502$ $13.50686390$ 1.773903022 \( \frac{3500231839}{331776} a - \frac{9525829495}{82944} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 8433891771 a - 91965905486\) , \( -1365231161498006 a + 14886925682200652\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(8433891771a-91965905486\right){x}-1365231161498006a+14886925682200652$
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  *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.