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Results (32 matches)

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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
15.1-a1 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.172294519$ $2.547989231$ 1.370958724 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -68780293 a - 318003982\) , \( 1319401941438 a + 6100222396500\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-68780293a-318003982\right){x}+1319401941438a+6100222396500$
15.1-a2 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.756712307$ $10.19195692$ 1.370958724 \( -\frac{1}{15} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -13023 a - 60202\) , \( -294878872 a - 1363365200\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-13023a-60202\right){x}-294878872a-1363365200$
15.1-a3 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.378356153$ $2.547989231$ 1.370958724 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 21867472 a + 101103728\) , \( 67141172125 a + 310425556510\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(21867472a+101103728\right){x}+67141172125a+310425556510$
15.1-a4 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.689178076$ $10.19195692$ 1.370958724 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -6264593 a - 28964182\) , \( 8918562808 a + 41234755600\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-6264593a-28964182\right){x}+8918562808a+41234755600$
15.1-a5 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.378356153$ $10.19195692$ 1.370958724 \( \frac{13997521}{225} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -3138808 a - 14512192\) , \( -6764057685 a - 31273454190\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-3138808a-14512192\right){x}-6764057685a-31273454190$
15.1-a6 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.344589038$ $10.19195692$ 1.370958724 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -84409218 a - 390263932\) , \( 954779057783 a + 4414397469850\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-84409218a-390263932\right){x}+954779057783a+4414397469850$
15.1-a7 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.756712307$ $2.547989231$ 1.370958724 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -50025583 a - 231292042\) , \( -436078729470 a - 2016199270740\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-50025583a-231292042\right){x}-436078729470a-2016199270740$
15.1-a8 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.172294519$ $10.19195692$ 1.370958724 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -1350352143 a - 6243319882\) , \( 61135112671028 a + 282656688470200\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-1350352143a-6243319882\right){x}+61135112671028a+282656688470200$
15.1-b1 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.490422220$ 3.063059717 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -72173 a - 333684\) , \( -45020158 a - 208149599\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-72173a-333684\right){x}-45020158a-208149599$
15.1-b2 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $31.38702211$ 3.063059717 \( -\frac{1}{15} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -13 a - 54\) , \( 9992 a + 46191\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-13a-54\right){x}+9992a+46191$
15.1-b3 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.961688882$ 3.063059717 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( 22947 a + 106101\) , \( -2227705 a - 10299746\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22947a+106101\right){x}-2227705a-10299746$
15.1-b4 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.846755528$ 3.063059717 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -6573 a - 30384\) , \( -318778 a - 1473869\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-6573a-30384\right){x}-318778a-1473869$
15.1-b5 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $31.38702211$ 3.063059717 \( \frac{13997521}{225} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -3293 a - 15219\) , \( 222095 a + 1026844\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-3293a-15219\right){x}+222095a+1026844$
15.1-b6 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.961688882$ 3.063059717 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -88573 a - 409509\) , \( -32665003 a - 151025844\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-88573a-409509\right){x}-32665003a-151025844$
15.1-b7 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $31.38702211$ 3.063059717 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -52493 a - 242694\) , \( 14698280 a + 67957129\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-52493a-242694\right){x}+14698280a+67957129$
15.1-b8 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.490422220$ 3.063059717 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -1416973 a - 6551334\) , \( -2081450248 a - 9623533989\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-1416973a-6551334\right){x}-2081450248a-9623533989$
15.1-c1 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.617916422$ $0.490422220$ 1.002354292 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
15.1-c2 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.654479105$ $31.38702211$ 1.002354292 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
15.1-c3 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $5.235832845$ $1.961688882$ 1.002354292 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
15.1-c4 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $2.617916422$ $7.846755528$ 1.002354292 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
15.1-c5 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1.308958211$ $31.38702211$ 1.002354292 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
15.1-c6 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.308958211$ $1.961688882$ 1.002354292 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
15.1-c7 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.654479105$ $31.38702211$ 1.002354292 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
15.1-c8 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.617916422$ $0.490422220$ 1.002354292 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
15.1-d1 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 0.994633150 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -10235 a - 47290\) , \( 2386570 a + 11034280\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-10235a-47290\right){x}+2386570a+11034280$
15.1-d2 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 0.994633150 \( -\frac{1}{15} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -5 a + 10\) , \( -540 a - 2460\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-5a+10\right){x}-540a-2460$
15.1-d3 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 0.994633150 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( 3250 a + 15060\) , \( 124193 a + 574242\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(3250a+15060\right){x}+124193a+574242$
15.1-d4 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 0.994633150 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -935 a - 4290\) , \( 15500 a + 71700\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-935a-4290\right){x}+15500a+71700$
15.1-d5 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 0.994633150 \( \frac{13997521}{225} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -470 a - 2140\) , \( -12617 a - 58298\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-470a-2140\right){x}-12617a-58298$
15.1-d6 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 0.994633150 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -12560 a - 58040\) , \( 1723275 a + 7967550\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-12560a-58040\right){x}+1723275a+7967550$
15.1-d7 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 0.994633150 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -7445 a - 34390\) , \( -796682 a - 3683408\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-7445a-34390\right){x}-796682a-3683408$
15.1-d8 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 0.994633150 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -200885 a - 928790\) , \( 110782080 a + 512198220\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-200885a-928790\right){x}+110782080a+512198220$
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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.