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Results (13 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
12800.4-a1 12800.4-a \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.161293589$ $4.117323585$ 4.016086598 \( -\frac{10752}{5} a - \frac{73216}{5} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 3 a - 1\) , \( -a - 1\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(3a-1\right){x}-a-1$
12800.4-b1 12800.4-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/4\Z$ $1$ $1.803516140$ 1.363330055 \( \frac{251566}{5} a - \frac{1108938}{5} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -28 a + 8\) , \( 64 a - 96\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-28a+8\right){x}+64a-96$
12800.4-b2 12800.4-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.803516140$ 1.363330055 \( -\frac{251566}{5} a - \frac{857372}{5} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 8 a + 32\) , \( 76 a - 72\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(8a+32\right){x}+76a-72$
12800.4-b3 12800.4-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.803516140$ 1.363330055 \( \frac{19652}{25} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -6 a + 11\) , \( 7 a - 13\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-6a+11\right){x}+7a-13$
12800.4-b4 12800.4-b \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.901758070$ 1.363330055 \( \frac{2185454}{625} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 34 a - 69\) , \( 127 a - 125\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(34a-69\right){x}+127a-125$
12800.4-c1 12800.4-c \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.161981579$ $0.599237495$ 4.108976077 \( \frac{12459008}{78125} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -31 a + 61\) , \( 367 a - 465\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a+61\right){x}+367a-465$
12800.4-d1 12800.4-d \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $2.004700957$ 3.030822964 \( -\frac{2249728}{5} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 17 a - 35\) , \( 41 a - 63\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(17a-35\right){x}+41a-63$
12800.4-e1 12800.4-e \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.574683819$ $2.548780403$ 4.428966097 \( \frac{51712}{125} a + \frac{841216}{125} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a + 9\) , \( 8 a - 5\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(2a+9\right){x}+8a-5$
12800.4-f1 12800.4-f \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.312331464$ $4.730000215$ 4.467019669 \( -\frac{1024}{5} a + \frac{2048}{5} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1\) , \( -a - 1\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1\right){x}-a-1$
12800.4-g1 12800.4-g \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.059560260$ 3.203809084 \( \frac{237276}{625} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 13 a - 26\) , \( -34 a - 68\bigr] \) ${y}^2={x}^{3}+\left(13a-26\right){x}-34a-68$
12800.4-g2 12800.4-g \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.119120521$ 3.203809084 \( \frac{148176}{25} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -7 a + 14\) , \( -6 a - 12\bigr] \) ${y}^2={x}^{3}+\left(-7a+14\right){x}-6a-12$
12800.4-g3 12800.4-g \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.238241043$ 3.203809084 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -2 a + 4\) , \( a + 2\bigr] \) ${y}^2={x}^{3}+\left(-2a+4\right){x}+a+2$
12800.4-g4 12800.4-g \(\Q(\sqrt{-7}) \) \( 2^{9} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.059560260$ 3.203809084 \( \frac{132304644}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -107 a + 214\) , \( -426 a - 852\bigr] \) ${y}^2={x}^{3}+\left(-107a+214\right){x}-426a-852$
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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.