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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 \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.490422220$ 0.856151218 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
75.1-a2 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $31.38702211$ 0.856151218 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
75.1-a3 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $1.961688882$ 0.856151218 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
75.1-a4 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $7.846755528$ 0.856151218 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
75.1-a5 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $31.38702211$ 0.856151218 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
75.1-a6 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.961688882$ 0.856151218 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
75.1-a7 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $31.38702211$ 0.856151218 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
75.1-a8 75.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.490422220$ 0.856151218 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
75.1-b1 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.172294519$ $2.547989231$ 1.532778450 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 552 a - 1536\) , \( -20014 a + 55870\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(552a-1536\right){x}-20014a+55870$
75.1-b2 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.689178076$ $10.19195692$ 1.532778450 \( -\frac{1}{15} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 2 a + 4\) , \( 6 a - 10\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+4\right){x}+6a-10$
75.1-b3 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.344589038$ $2.547989231$ 1.532778450 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -173 a + 494\) , \( -1016 a + 2846\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-173a+494\right){x}-1016a+2846$
75.1-b4 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.172294519$ $10.19195692$ 1.532778450 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 52 a - 136\) , \( -134 a + 380\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(52a-136\right){x}-134a+380$
75.1-b5 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.344589038$ $10.19195692$ 1.532778450 \( \frac{13997521}{225} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 27 a - 66\) , \( 104 a - 284\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(27a-66\right){x}+104a-284$
75.1-b6 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.086147259$ $10.19195692$ 1.532778450 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 677 a - 1886\) , \( -14484 a + 40430\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(677a-1886\right){x}-14484a+40430$
75.1-b7 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.689178076$ $2.547989231$ 1.532778450 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 402 a - 1116\) , \( 6614 a - 18464\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(402a-1116\right){x}+6614a-18464$
75.1-b8 75.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.172294519$ $10.19195692$ 1.532778450 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 10802 a - 30236\) , \( -927354 a + 2588690\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(10802a-30236\right){x}-927354a+2588690$
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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.