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Results (4 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
12.2-a1 12.2-a \(\Q(\sqrt{85}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.126569341$ $19.44068589$ 1.601333870 \( -\frac{4133602}{729} a + \frac{34766975}{972} \) \( \bigl[a\) , \( 0\) , \( a + 1\) , \( -3749 a - 15408\) , \( 223496 a + 918518\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-3749a-15408\right){x}+223496a+918518$
12.2-a2 12.2-a \(\Q(\sqrt{85}) \) \( 2^{2} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.253138682$ $9.720342945$ 1.601333870 \( \frac{2087352478285}{531441} a + \frac{5719028825027}{354294} \) \( \bigl[a\) , \( 0\) , \( a + 1\) , \( -57679 a - 237048\) , \( 16063422 a + 66017006\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-57679a-237048\right){x}+16063422a+66017006$
12.2-b1 12.2-b \(\Q(\sqrt{85}) \) \( 2^{2} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $19.44068589$ 2.108638445 \( -\frac{4133602}{729} a + \frac{34766975}{972} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -3 a - 4\) , \( -a + 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-4\right){x}-a+3$
12.2-b2 12.2-b \(\Q(\sqrt{85}) \) \( 2^{2} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.720342945$ 2.108638445 \( \frac{2087352478285}{531441} a + \frac{5719028825027}{354294} \) \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13 a - 44\) , \( 37 a + 161\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-13a-44\right){x}+37a+161$
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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.