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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
35.1-a1 35.1-a \(\Q(\sqrt{105}) \) \( 5 \cdot 7 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $3.380268306$ $0.494084210$ 2.607819218 \( -\frac{250523582464}{13671875} \) \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -86155 a - 398325\) , \( -32460825 a - 150081819\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-86155a-398325\right){x}-32460825a-150081819$
35.1-b1 35.1-b \(\Q(\sqrt{105}) \) \( 5 \cdot 7 \) 0 $\Z/3\Z$ $\mathrm{SU}(2)$ $1$ $4.862220259$ 1.898016442 \( -\frac{250523582464}{13671875} \) \( \bigl[0\) , \( 1\) , \( a\) , \( -12214 a - 56473\) , \( 1735781 a + 8025336\bigr] \) ${y}^2+a{y}={x}^{3}+{x}^{2}+\left(-12214a-56473\right){x}+1735781a+8025336$
35.1-c1 35.1-c \(\Q(\sqrt{105}) \) \( 5 \cdot 7 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.040819755$ $4.862220259$ 1.394578218 \( -\frac{250523582464}{13671875} \) \( \bigl[0\) , \( a\) , \( a\) , \( 1445 a - 8134\) , \( -73135 a + 411269\bigr] \) ${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(1445a-8134\right){x}-73135a+411269$
35.1-d1 35.1-d \(\Q(\sqrt{105}) \) \( 5 \cdot 7 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $7.121947793$ $0.494084210$ 2.747230492 \( -\frac{250523582464}{13671875} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-131{x}-650$
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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.