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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
121.2-a1 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.977037162$ 0.907156231 \( \frac{65043647691776021422241682240608199}{672749994932560009201} a^{3} - \frac{96086378758944288871120259445713823}{672749994932560009201} a^{2} - \frac{149272758287266592627239816194505540}{672749994932560009201} a + \frac{136285563785147203403128081725176307}{672749994932560009201} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -16720 a^{3} + 24671 a^{2} + 38355 a - 35026\) , \( -1387530 a^{3} + 2049643 a^{2} + 3184128 a - 2907368\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-16720a^{3}+24671a^{2}+38355a-35026\right){x}-1387530a^{3}+2049643a^{2}+3184128a-2907368$
121.2-a2 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.977037162$ 0.907156231 \( \frac{14815453720893204190606653322213433}{672749994932560009201} a^{3} + \frac{16227277346275063258271923882892191}{672749994932560009201} a^{2} - \frac{10445444538071858598456854931137724}{672749994932560009201} a - \frac{7070823387240416175142678808535331}{672749994932560009201} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -1280 a^{3} + 1411 a^{2} + 2605 a - 2256\) , \( -23574 a^{3} + 24161 a^{2} + 47564 a - 38706\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-1280a^{3}+1411a^{2}+2605a-2256\right){x}-23574a^{3}+24161a^{2}+47564a-38706$
121.2-a3 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.908148650$ 0.907156231 \( \frac{187129494303327793}{25937424601} a^{3} - \frac{187129494303327793}{25937424601} a^{2} - \frac{374258988606655586}{25937424601} a + \frac{306942795920590510}{25937424601} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -1040 a^{3} + 1521 a^{2} + 2360 a - 2201\) , \( -22150 a^{3} + 32546 a^{2} + 50676 a - 46325\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-1040a^{3}+1521a^{2}+2360a-2201\right){x}-22150a^{3}+32546a^{2}+50676a-46325$
121.2-a4 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $610.6482266$ 0.907156231 \( -\frac{866644489227232719}{14641} a^{3} + \frac{227235771577839273}{14641} a^{2} + \frac{2767753838637694562}{14641} a + \frac{1175276275743734610}{14641} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -325 a^{3} + 501 a^{2} + 730 a - 741\) , \( 3802 a^{3} - 5685 a^{2} - 8677 a + 8158\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-325a^{3}+501a^{2}+730a-741\right){x}+3802a^{3}-5685a^{2}-8677a+8158$
121.2-a5 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.908148650$ 0.907156231 \( -\frac{1836359985305255}{161051} a^{3} + \frac{1836359985305255}{161051} a^{2} + \frac{3672719970610510}{161051} a + \frac{1134932348617143}{161051} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -45 a^{3} + 81 a^{2} + 95 a - 146\) , \( -374 a^{3} + 588 a^{2} + 831 a - 909\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-45a^{3}+81a^{2}+95a-146\right){x}-374a^{3}+588a^{2}+831a-909$
121.2-a6 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $610.6482266$ 0.907156231 \( -\frac{471588346693397041}{14641} a^{3} + \frac{1110997064342790487}{14641} a^{2} - \frac{91288166796435042}{14641} a - \frac{347893734670610050}{14641} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -35 a^{3} + 41 a^{2} + 80 a - 71\) , \( -50 a^{3} + 83 a^{2} + 109 a - 102\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-35a^{3}+41a^{2}+80a-71\right){x}-50a^{3}+83a^{2}+109a-102$
121.2-a7 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/2\Z\oplus\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $2442.592906$ 0.907156231 \( -\frac{765788765}{121} a^{3} + \frac{765788765}{121} a^{2} + \frac{1531577530}{121} a + \frac{490956721}{121} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( -20 a^{3} + 31 a^{2} + 45 a - 46\) , \( 50 a^{3} - 75 a^{2} - 114 a + 108\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(-20a^{3}+31a^{2}+45a-46\right){x}+50a^{3}-75a^{2}-114a+108$
121.2-a8 121.2-a 4.4.725.1 \( 11^{2} \) 0 $\Z/10\Z$ $\mathrm{SU}(2)$ $1$ $2442.592906$ 0.907156231 \( -\frac{22625}{11} a^{3} + \frac{22625}{11} a^{2} + \frac{45250}{11} a + \frac{13758}{11} \) \( \bigl[a^{2}\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - a + 2\) , \( a^{2} - 1\) , \( 2 a^{3} - 2 a^{2} - 4 a + 3\bigr] \) ${y}^2+a^{2}{x}{y}+\left(a^{3}-a^{2}-a+2\right){y}={x}^{3}+\left(a^{3}-a^{2}-2a+1\right){x}^{2}+\left(a^{2}-1\right){x}+2a^{3}-2a^{2}-4a+3$
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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.