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Results (24 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
28672.6-a1 28672.6-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $1.302440417$ $1.946210420$ 3.832292328 \( \frac{5384}{343} a + \frac{591184}{343} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -4 a + 13\) , \( 3 a - 1\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-4a+13\right){x}+3a-1$
28672.6-a2 28672.6-a \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.651220208$ $1.946210420$ 3.832292328 \( \frac{3358624}{49} a + \frac{16414176}{49} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -26 a + 4\) , \( -64 a + 80\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-26a+4\right){x}-64a+80$
28672.6-b1 28672.6-b \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.650508069$ 2.003595771 \( -\frac{1592}{7} a + \frac{5328}{7} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 4\) , \( -8\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(4a-4\right){x}-8$
28672.6-b2 28672.6-b \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $5.301016139$ 2.003595771 \( \frac{6752}{7} a + \frac{22048}{7} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-a+1\right){x}$
28672.6-c1 28672.6-c \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $2$ $\Z/2\Z$ $0.116088918$ $2.262632169$ 6.353831277 \( -992 a + \frac{26528}{7} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -7 a + 1\) , \( 3 a - 1\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a+1\right){x}+3a-1$
28672.6-c2 28672.6-c \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $2$ $\Z/2\Z$ $0.464355675$ $4.525264338$ 6.353831277 \( \frac{60864}{7} a + \frac{88064}{7} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2 a + 1\) , \( -3 a + 5\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a+1\right){x}-3a+5$
28672.6-d1 28672.6-d \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.199845100$ 2.418855533 \( -992 a + \frac{26528}{7} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 4 a - 5\) , \( -3 a - 2\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(4a-5\right){x}-3a-2$
28672.6-d2 28672.6-d \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.199845100$ 2.418855533 \( \frac{60864}{7} a + \frac{88064}{7} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a + 3\) , \( a - 5\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(4a+3\right){x}+a-5$
28672.6-e1 28672.6-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.420540580$ $3.748384459$ 4.766427658 \( -\frac{1592}{7} a + \frac{5328}{7} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -a + 3\) , \( -a + 3\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-a+3\right){x}-a+3$
28672.6-e2 28672.6-e \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.841081161$ $3.748384459$ 4.766427658 \( \frac{6752}{7} a + \frac{22048}{7} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a - 1\) , \( 3 a - 1\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a-1\right){x}+3a-1$
28672.6-f1 28672.6-f \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $1.143477997$ $1.376178586$ 4.758209668 \( \frac{5384}{343} a + \frac{591184}{343} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 17 a - 19\) , \( 9 a - 11\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(17a-19\right){x}+9a-11$
28672.6-f2 28672.6-f \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $2.286955994$ $2.752357172$ 4.758209668 \( \frac{3358624}{49} a + \frac{16414176}{49} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 12 a - 14\) , \( 26 a - 14\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(12a-14\right){x}+26a-14$
28672.6-g1 28672.6-g \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.486703406$ $2.650508069$ 3.900627548 \( -\frac{1592}{7} a + \frac{5328}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 4\) , \( 8\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(4a-4\right){x}+8$
28672.6-g2 28672.6-g \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.973406812$ $5.301016139$ 3.900627548 \( \frac{6752}{7} a + \frac{22048}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
28672.6-h1 28672.6-h \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.251503967$ $1.946210420$ 4.440141962 \( \frac{5384}{343} a + \frac{591184}{343} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a + 13\) , \( -3 a + 1\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+13\right){x}-3a+1$
28672.6-h2 28672.6-h \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.503007935$ $1.946210420$ 4.440141962 \( \frac{3358624}{49} a + \frac{16414176}{49} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -26 a + 4\) , \( 64 a - 80\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-26a+4\right){x}+64a-80$
28672.6-i1 28672.6-i \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.377406479$ $2.262632169$ 5.164095586 \( -992 a + \frac{26528}{7} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -7 a + 1\) , \( -3 a + 1\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-7a+1\right){x}-3a+1$
28672.6-i2 28672.6-i \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.754812959$ $4.525264338$ 5.164095586 \( \frac{60864}{7} a + \frac{88064}{7} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -2 a + 1\) , \( 3 a - 5\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+1\right){x}+3a-5$
28672.6-j1 28672.6-j \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.199845100$ 2.418855533 \( -992 a + \frac{26528}{7} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 4 a - 5\) , \( 3 a + 2\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(4a-5\right){x}+3a+2$
28672.6-j2 28672.6-j \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.199845100$ 2.418855533 \( \frac{60864}{7} a + \frac{88064}{7} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a + 3\) , \( -a + 5\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(4a+3\right){x}-a+5$
28672.6-k1 28672.6-k \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $1.376178586$ 3.120879684 \( \frac{5384}{343} a + \frac{591184}{343} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 17 a - 19\) , \( -9 a + 11\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(17a-19\right){x}-9a+11$
28672.6-k2 28672.6-k \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $0$ $\Z/2\Z$ $1$ $2.752357172$ 3.120879684 \( \frac{3358624}{49} a + \frac{16414176}{49} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 12 a - 14\) , \( -26 a + 14\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(12a-14\right){x}-26a+14$
28672.6-l1 28672.6-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.973140417$ $3.748384459$ 5.514810713 \( -\frac{1592}{7} a + \frac{5328}{7} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -a + 3\) , \( a - 3\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-a+3\right){x}+a-3$
28672.6-l2 28672.6-l \(\Q(\sqrt{-7}) \) \( 2^{12} \cdot 7 \) $1$ $\Z/2\Z$ $0.486570208$ $3.748384459$ 5.514810713 \( \frac{6752}{7} a + \frac{22048}{7} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a - 1\) , \( -3 a + 1\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-1\right){x}-3a+1$
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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.