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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
100156.5-a1 100156.5-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $0$ $\Z/2\Z$ $1$ $0.203061397$ 0.937900421 \( \frac{804510685664741}{983059984928} a - \frac{667729823206917}{983059984928} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 389 a - 991\) , \( -3151 a + 17152\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(389a-991\right){x}-3151a+17152$
100156.5-a2 100156.5-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $0$ $\Z/2\Z$ $1$ $0.406122795$ 0.937900421 \( -\frac{1089514891873}{179479552} a + \frac{10168308517}{2804368} \) \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -411 a + 289\) , \( -1999 a + 3392\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-411a+289\right){x}-1999a+3392$
100156.5-b1 100156.5-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $0$ $\Z/2\Z$ $1$ $0.298093572$ 1.376835233 \( \frac{2913552868954332}{3341024655409} a - \frac{9105588620662571}{6682049310818} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -491 a + 409\) , \( -368 a + 6106\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-491a+409\right){x}-368a+6106$
100156.5-b2 100156.5-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $0$ $\Z/2\Z$ $1$ $0.596187144$ 1.376835233 \( -\frac{5321822571516}{1827847} a + \frac{24111647375183}{7311388} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( -541 a + 489\) , \( -844 a + 5182\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-541a+489\right){x}-844a+5182$
100156.5-c1 100156.5-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $1$ $\Z/2\Z$ $1.760386406$ $0.378236563$ 3.075394794 \( \frac{275361962643}{34353508} a - \frac{64083232890}{8588377} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 525 a - 203\) , \( -2793 a - 1568\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(525a-203\right){x}-2793a-1568$
100156.5-c2 100156.5-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $1$ $\Z/2\Z$ $1.173590937$ $0.189118281$ 3.075394794 \( \frac{1454621964199278075}{1453413909279556} a + \frac{3568835637322210611}{2906827818559112} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -929 a + 1539\) , \( -13161 a + 1058\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-929a+1539\right){x}-13161a+1058$
100156.5-c3 100156.5-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $1$ $\Z/2\Z$ $3.520772813$ $0.189118281$ 3.075394794 \( -\frac{637509743623817073}{147520438988258} a + \frac{202953104452384443}{147520438988258} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 1015 a + 777\) , \( -22687 a + 28616\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1015a+777\right){x}-22687a+28616$
100156.5-c4 100156.5-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $1$ $\Z/2\Z$ $0.586795468$ $0.378236563$ 3.075394794 \( -\frac{8487617049675}{152494664} a + \frac{53427433970061}{1219957312} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( -649 a + 699\) , \( 839 a + 6098\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-649a+699\right){x}+839a+6098$
100156.5-d1 100156.5-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 7^{3} \cdot 73 \) $0$ $\mathsf{trivial}$ $1$ $0.848608682$ 4.899444515 \( -\frac{98864793}{16352} a + \frac{45763083}{8176} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 6 a + 83\) , \( 361 a - 153\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(6a+83\right){x}+361a-153$
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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.