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Results (16 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
75.1-a1 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.471082268 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -109\) , \( 770\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-109{x}+770$
75.1-a2 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.471082268 \( -\frac{1}{15} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 227 a - 390\) , \( 392730 a - 680227\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(227a-390\right){x}+392730a-680227$
75.1-a3 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.471082268 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 36\) , \( 63\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+36{x}+63$
75.1-a4 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.471082268 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -9\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-9{x}$
75.1-a5 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.471082268 \( \frac{13997521}{225} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 281 a - 486\) , \( 3516 a - 6090\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(281a-486\right){x}+3516a-6090$
75.1-a6 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.471082268 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -134\) , \( 525\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-134{x}+525$
75.1-a7 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 1.471082268 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 4481 a - 7761\) , \( 217866 a - 377355\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(4481a-7761\right){x}+217866a-377355$
75.1-a8 75.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $10.19195692$ 1.471082268 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -2159\) , \( 37380\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}-2159{x}+37380$
75.1-b1 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.201251375$ $0.490422220$ 0.736355203 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
75.1-b2 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.325078210$ $31.38702211$ 0.736355203 \( -\frac{1}{15} \) \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 225 a - 391\) , \( -392504 a + 679835\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(225a-391\right){x}-392504a+679835$
75.1-b3 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $2.600625687$ $1.961688882$ 0.736355203 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
75.1-b4 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1.300312843$ $7.846755528$ 0.736355203 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
75.1-b5 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $0.650156421$ $31.38702211$ 0.736355203 \( \frac{13997521}{225} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 281 a - 486\) , \( -3516 a + 6090\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(281a-486\right){x}-3516a+6090$
75.1-b6 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.600625687$ $1.961688882$ 0.736355203 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
75.1-b7 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $1.300312843$ $31.38702211$ 0.736355203 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 4481 a - 7761\) , \( -217866 a + 377355\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(4481a-7761\right){x}-217866a+377355$
75.1-b8 75.1-b \(\Q(\sqrt{3}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $5.201251375$ $0.490422220$ 0.736355203 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
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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.