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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
242.1-a1 242.1-a \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.418339135$ $9.831379401$ 6.354298938 \( \frac{704969}{484} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -10 a + 29\) , \( -9 a + 29\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-10a+29\right){x}-9a+29$
242.1-a2 242.1-a \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.836678270$ $9.831379401$ 6.354298938 \( \frac{59776471}{29282} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 30 a - 121\) , \( 147 a - 555\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(30a-121\right){x}+147a-555$
242.1-a3 242.1-a \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $9.673356541$ $2.457844850$ 6.354298938 \( -\frac{64805448747361}{428717762} a + \frac{138290588033512}{214358881} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 425 a - 1601\) , \( 10255 a - 38379\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(425a-1601\right){x}+10255a-38379$
242.1-a4 242.1-a \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.418339135$ $9.831379401$ 6.354298938 \( \frac{64805448747361}{428717762} a + \frac{138290588033512}{214358881} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( 275 a - 1041\) , \( -4217 a + 15773\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(275a-1041\right){x}-4217a+15773$
242.1-b1 242.1-b \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.418339135$ $9.831379401$ 6.354298938 \( \frac{704969}{484} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 8 a + 29\) , \( 8 a + 29\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(8a+29\right){x}+8a+29$
242.1-b2 242.1-b \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.836678270$ $9.831379401$ 6.354298938 \( \frac{59776471}{29282} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -32 a - 121\) , \( -148 a - 555\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-32a-121\right){x}-148a-555$
242.1-b3 242.1-b \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.418339135$ $9.831379401$ 6.354298938 \( -\frac{64805448747361}{428717762} a + \frac{138290588033512}{214358881} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -277 a - 1041\) , \( 4216 a + 15773\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-277a-1041\right){x}+4216a+15773$
242.1-b4 242.1-b \(\Q(\sqrt{14}) \) \( 2 \cdot 11^{2} \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $9.673356541$ $2.457844850$ 6.354298938 \( \frac{64805448747361}{428717762} a + \frac{138290588033512}{214358881} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -427 a - 1601\) , \( -10256 a - 38379\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-427a-1601\right){x}-10256a-38379$
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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.