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Results (8 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
3.2-a1 3.2-a \(\Q(\sqrt{85}) \) \( 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.699459757$ 1.365607129 \( -\frac{732096671152080845}{81} a + \frac{1246949079628698820}{27} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -10332 a - 42522\) , \( -1271183 a - 5224453\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-10332a-42522\right){x}-1271183a-5224453$
3.2-a2 3.2-a \(\Q(\sqrt{85}) \) \( 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.295137819$ 1.365607129 \( -\frac{25207270205}{531441} a + \frac{42974373355}{177147} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 198 a + 813\) , \( -7340 a - 30166\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(198a+813\right){x}-7340a-30166$
3.2-a3 3.2-a \(\Q(\sqrt{85}) \) \( 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $25.18055127$ 1.365607129 \( \frac{505895}{729} a + \frac{1119530}{243} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -127 a - 522\) , \( -2077 a - 8536\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-127a-522\right){x}-2077a-8536$
3.2-a4 3.2-a \(\Q(\sqrt{85}) \) \( 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.797839030$ 1.365607129 \( \frac{392415680105}{9} a + \frac{538445689895}{3} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -10342 a - 42507\) , \( -1270240 a - 5220400\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-10342a-42507\right){x}-1270240a-5220400$
3.2-b1 3.2-b \(\Q(\sqrt{85}) \) \( 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $8.145025583$ $0.699459757$ 1.235878333 \( -\frac{732096671152080845}{81} a + \frac{1246949079628698820}{27} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -13050 a - 53636\) , \( -1785556 a - 7338231\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-13050a-53636\right){x}-1785556a-7338231$
3.2-b2 3.2-b \(\Q(\sqrt{85}) \) \( 3 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $2.715008527$ $6.295137819$ 1.235878333 \( -\frac{25207270205}{531441} a + \frac{42974373355}{177147} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 245 a + 1004\) , \( -10714 a - 44034\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(245a+1004\right){x}-10714a-44034$
3.2-b3 3.2-b \(\Q(\sqrt{85}) \) \( 3 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $1.357504263$ $25.18055127$ 1.235878333 \( \frac{505895}{729} a + \frac{1119530}{243} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -165 a - 681\) , \( -2743 a - 11275\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-165a-681\right){x}-2743a-11275$
3.2-b4 3.2-b \(\Q(\sqrt{85}) \) \( 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.072512791$ $2.797839030$ 1.235878333 \( \frac{392415680105}{9} a + \frac{538445689895}{3} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -13055 a - 53656\) , \( -1784186 a - 7332600\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-13055a-53656\right){x}-1784186a-7332600$
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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.