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Results (30 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
25600.7-a1 25600.7-a \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $2.365000107$ 1.787772038 \( -\frac{1024}{5} a + \frac{2048}{5} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 5\) , \( a + 5\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+5\right){x}+a+5$
25600.7-b1 25600.7-b \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.577386419$ $4.730000215$ 4.128941187 \( \frac{1024}{5} a + \frac{1024}{5} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 1\) , \( -a + 1\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+1\right){x}-a+1$
25600.7-c1 25600.7-c \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.059560260$ 1.601904542 \( \frac{237276}{625} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -13 a - 13\) , \( -34 a + 102\bigr] \) ${y}^2={x}^{3}+\left(-13a-13\right){x}-34a+102$
25600.7-c2 25600.7-c \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.119120521$ 1.601904542 \( \frac{148176}{25} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a + 7\) , \( -6 a + 18\bigr] \) ${y}^2={x}^{3}+\left(7a+7\right){x}-6a+18$
25600.7-c3 25600.7-c \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.238241043$ 1.601904542 \( \frac{55296}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 2\) , \( a - 3\bigr] \) ${y}^2={x}^{3}+\left(2a+2\right){x}+a-3$
25600.7-c4 25600.7-c \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.059560260$ 1.601904542 \( \frac{132304644}{5} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 107 a + 107\) , \( -426 a + 1278\bigr] \) ${y}^2={x}^{3}+\left(107a+107\right){x}-426a+1278$
25600.7-d1 25600.7-d \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $2.548780403$ 1.926696884 \( -\frac{51712}{125} a + \frac{892928}{125} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -2 a + 11\) , \( 8 a - 3\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-2a+11\right){x}+8a-3$
25600.7-e1 25600.7-e \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.349999499$ $4.532128131$ 4.796346722 \( -\frac{5632}{5} a + \frac{17408}{5} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 2 a - 1\) , \( -1\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(2a-1\right){x}-1$
25600.7-f1 25600.7-f \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.448706508$ $2.152771205$ 4.381193866 \( -\frac{110592}{125} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 8\) , \( 10 a - 12\bigr] \) ${y}^2={x}^{3}+\left(4a-8\right){x}+10a-12$
25600.7-g1 25600.7-g \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $3.283662346$ $0.420833872$ 4.178401309 \( -\frac{115501303}{25600} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -162 a - 163\) , \( 1661 a + 462\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-162a-163\right){x}+1661a+462$
25600.7-g2 25600.7-g \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z$ $1.641831173$ $0.420833872$ 4.178401309 \( \frac{2083468303}{5242880} a - \frac{14990614869}{5242880} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 88 a + 216\) , \( -1332 a + 2044\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(88a+216\right){x}-1332a+2044$
25600.7-g3 25600.7-g \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z$ $1.641831173$ $0.420833872$ 4.178401309 \( -\frac{2083468303}{5242880} a - \frac{6453573283}{2621440} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 184 a + 56\) , \( 112 a - 2288\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(184a+56\right){x}+112a-2288$
25600.7-g4 25600.7-g \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/4\Z$ $6.567324693$ $0.210416936$ 4.178401309 \( \frac{544737993463}{20000} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -2722 a - 2723\) , \( 101501 a + 22478\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-2722a-2723\right){x}+101501a+22478$
25600.7-h1 25600.7-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/4\Z$ $1$ $0.856375589$ 2.589436387 \( -\frac{5212389}{1250} a - \frac{3938057}{1250} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -34 a + 93\) , \( 189 a + 206\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-34a+93\right){x}+189a+206$
25600.7-h2 25600.7-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.712751179$ 2.589436387 \( \frac{220731}{100} a - \frac{244729}{100} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 6 a + 13\) , \( -11 a + 30\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(6a+13\right){x}-11a+30$
25600.7-h3 25600.7-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.712751179$ 2.589436387 \( -\frac{85169}{80} a - \frac{36501}{80} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a - 8\) , \( -20 a - 4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a-8\right){x}-20a-4$
25600.7-h4 25600.7-h \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.712751179$ 2.589436387 \( -\frac{92108807}{10} a + \frac{519677}{10} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -47 a + 66\) , \( 2 a + 228\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-47a+66\right){x}+2a+228$
25600.7-i1 25600.7-i \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.803516140$ 2.726660110 \( \frac{251566}{5} a - \frac{1108938}{5} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -8 a + 40\) , \( 76 a - 4\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-8a+40\right){x}+76a-4$
25600.7-i2 25600.7-i \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.803516140$ 2.726660110 \( -\frac{251566}{5} a - \frac{857372}{5} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 28 a - 20\) , \( 64 a + 32\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(28a-20\right){x}+64a+32$
25600.7-i3 25600.7-i \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.803516140$ 2.726660110 \( \frac{19652}{25} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 6 a + 5\) , \( 7 a + 6\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(6a+5\right){x}+7a+6$
25600.7-i4 25600.7-i \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\Z/4\Z$ $1$ $0.901758070$ 2.726660110 \( \frac{2185454}{625} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -34 a - 35\) , \( 127 a - 2\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-34a-35\right){x}+127a-2$
25600.7-j1 25600.7-j \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $2.004700957$ 1.515411482 \( -\frac{2249728}{5} \) \( \bigl[0\) , \( a\) , \( 0\) , \( -17 a - 18\) , \( 41 a + 22\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-17a-18\right){x}+41a+22$
25600.7-k1 25600.7-k \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.574523216$ $2.952354725$ 5.128815624 \( \frac{8192}{5} \) \( \bigl[0\) , \( a\) , \( 0\) , \( 3 a + 2\) , \( a - 2\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(3a+2\right){x}+a-2$
25600.7-l1 25600.7-l \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $0.599237495$ 3.170866776 \( \frac{12459008}{78125} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 31 a + 30\) , \( 367 a + 98\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(31a+30\right){x}+367a+98$
25600.7-m1 25600.7-m \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $0$ $\mathsf{trivial}$ $1$ $3.694608880$ 2.792861796 \( -512 a - \frac{1024}{5} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a + 1\) , \( a - 1\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a+1\right){x}+a-1$
25600.7-n1 25600.7-n \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z$ $2.235297094$ $0.756969082$ 5.116280683 \( -\frac{20720464}{15625} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 36 a + 36\) , \( -140 a + 420\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(36a+36\right){x}-140a+420$
25600.7-n2 25600.7-n \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z$ $0.745099031$ $2.270907247$ 5.116280683 \( \frac{21296}{25} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4 a - 4\) , \( 4 a - 12\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a-4\right){x}+4a-12$
25600.7-n3 25600.7-n \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z$ $1.490198062$ $4.541814495$ 5.116280683 \( \frac{16384}{5} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( a + 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+1\right){x}$
25600.7-n4 25600.7-n \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\Z/2\Z$ $4.470594188$ $1.513938165$ 5.116280683 \( \frac{488095744}{125} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 41 a + 41\) , \( -116 a + 348\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(41a+41\right){x}-116a+348$
25600.7-o1 25600.7-o \(\Q(\sqrt{-7}) \) \( 2^{10} \cdot 5^{2} \) $1$ $\mathsf{trivial}$ $0.899275836$ $4.117323585$ 5.597819561 \( \frac{10752}{5} a - \frac{83968}{5} \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -3 a + 2\) , \( -a + 2\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-3a+2\right){x}-a+2$
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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.