Learn more

Refine search


Results (19 matches)

  Download to        
Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
71424.1-a1 71424.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\mathsf{trivial}$ $1.401922107$ $0.265892738$ 3.443417772 \( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -264 a - 456\) , \( 4776 a - 1812\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-264a-456\right){x}+4776a-1812$
71424.1-a2 71424.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\mathsf{trivial}$ $0.280384421$ $1.329463692$ 3.443417772 \( -\frac{24551}{62} a + \frac{45753}{31} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -24 a + 24\) , \( -24 a + 12\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-24a+24\right){x}-24a+12$
71424.1-a3 71424.1-a \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\mathsf{trivial}$ $7.009610537$ $0.053178547$ 3.443417772 \( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 26376 a + 36024\) , \( -4499544 a + 5180172\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(26376a+36024\right){x}-4499544a+5180172$
71424.1-b1 71424.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\Z/2\Z$ $0.296057380$ $2.356764957$ 3.222712205 \( -\frac{355344}{961} a + \frac{669360}{961} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 4\) , \( 12 a\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+4\right){x}+12a$
71424.1-b2 71424.1-b \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\Z/2\Z$ $0.592114760$ $4.713529915$ 3.222712205 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-a-1\right){x}$
71424.1-c1 71424.1-c \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\Z/2\Z$ $0.540606015$ $1.360678882$ 3.397550170 \( -\frac{355344}{961} a + \frac{669360}{961} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 21 a - 9\) , \( 24 a - 50\bigr] \) ${y}^2={x}^{3}+\left(21a-9\right){x}+24a-50$
71424.1-c2 71424.1-c \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\Z/2\Z$ $1.081212031$ $2.721357765$ 3.397550170 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -9 a + 6\) , \( 3 a - 8\bigr] \) ${y}^2={x}^{3}+\left(-9a+6\right){x}+3a-8$
71424.1-d1 71424.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\Z/2\Z$ $1$ $2.897089926$ 1.672635649 \( \frac{2998016}{93} a - \frac{425728}{93} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a - 12\) , \( -9 a + 9\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(6a-12\right){x}-9a+9$
71424.1-d2 71424.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\Z/4\Z$ $1$ $0.724272481$ 1.672635649 \( \frac{2499774004}{2770563} a + \frac{1516133908}{2770563} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -39 a + 93\) , \( 297 a - 144\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-39a+93\right){x}+297a-144$
71424.1-d3 71424.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.448544963$ 1.672635649 \( -\frac{4637360}{2883} a + \frac{2720576}{961} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 21 a - 27\) , \( 45 a - 36\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(21a-27\right){x}+45a-36$
71424.1-d4 71424.1-d \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\Z/2\Z$ $1$ $0.724272481$ 1.672635649 \( -\frac{1160560100}{279} a + \frac{385205612}{279} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 321 a - 387\) , \( 3009 a - 2328\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(321a-387\right){x}+3009a-2328$
71424.1-e1 71424.1-e \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\Z/2\Z$ $1$ $2.356764957$ 2.721357765 \( -\frac{355344}{961} a + \frac{669360}{961} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 4 a + 4\) , \( -12 a\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a+4\right){x}-12a$
71424.1-e2 71424.1-e \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\Z/2\Z$ $1$ $4.713529915$ 2.721357765 \( \frac{63744}{31} a + \frac{93696}{31} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-1\right){x}$
71424.1-f1 71424.1-f \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\mathsf{trivial}$ $1$ $0.727178501$ 1.679346813 \( -\frac{10618695}{29791} a - \frac{103188411}{59582} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 75 a - 96\) , \( 480 a - 358\bigr] \) ${y}^2={x}^{3}+\left(75a-96\right){x}+480a-358$
71424.1-f2 71424.1-f \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\mathsf{trivial}$ $1$ $0.727178501$ 1.679346813 \( \frac{44272737}{124} a + \frac{10648665}{248} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 195 a + 96\) , \( -864 a + 1826\bigr] \) ${y}^2={x}^{3}+\left(195a+96\right){x}-864a+1826$
71424.1-g1 71424.1-g \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $1$ $\mathsf{trivial}$ $0.274027341$ $1.622671209$ 4.107558749 \( -\frac{20086}{31} a - \frac{49116}{31} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 16\) , \( 52 a - 24\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+16\right){x}+52a-24$
71424.1-h1 71424.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\mathsf{trivial}$ $1$ $0.265892738$ 3.070264883 \( \frac{511363962461}{916132832} a + \frac{1018073036305}{916132832} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -455 a + 721\) , \( -4511 a + 2268\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-455a+721\right){x}-4511a+2268$
71424.1-h2 71424.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\mathsf{trivial}$ $1$ $1.329463692$ 3.070264883 \( -\frac{24551}{62} a + \frac{45753}{31} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a + 1\) , \( 49 a - 36\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(25a+1\right){x}+49a-36$
71424.1-h3 71424.1-h \(\Q(\sqrt{-3}) \) \( 2^{8} \cdot 3^{2} \cdot 31 \) $0$ $\mathsf{trivial}$ $1$ $0.053178547$ 3.070264883 \( -\frac{936087656892551}{1040187392} a + \frac{51401239062153}{520093696} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 36025 a - 62399\) , \( 4473169 a - 5216196\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(36025a-62399\right){x}+4473169a-5216196$
  Download to        

  *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.