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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
15.1-a7 15.1-a \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.756712307$ $2.547989231$ 1.370958724 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -50025583 a - 231292042\) , \( -436078729470 a - 2016199270740\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-50025583a-231292042\right){x}-436078729470a-2016199270740$
15.1-b7 15.1-b \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $31.38702211$ 3.063059717 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( -52493 a - 242694\) , \( 14698280 a + 67957129\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-52493a-242694\right){x}+14698280a+67957129$
15.1-c7 15.1-c \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.654479105$ $31.38702211$ 1.002354292 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
15.1-d7 15.1-d \(\Q(\sqrt{105}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.547989231$ 0.994633150 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -7445 a - 34390\) , \( -796682 a - 3683408\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}+\left(-7445a-34390\right){x}-796682a-3683408$
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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.