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Results (26 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
50700.2-a1 50700.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $0.104518806$ $1.208615532$ 2.917305948 \( -\frac{16022066761}{998400} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -52 a + 51\) , \( -124\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-52a+51\right){x}-124$
50700.2-a2 50700.2-a \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $0.209037613$ $0.604307766$ 2.917305948 \( \frac{68523370149961}{243360} \) \( \bigl[a + 1\) , \( a\) , \( 1\) , \( -852 a + 851\) , \( -9084\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-852a+851\right){x}-9084$
50700.2-b1 50700.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $1.175373745$ $0.635041399$ 3.447524680 \( \frac{99317171591}{106616250} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -97 a\) , \( -297\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}-97a{x}-297$
50700.2-b2 50700.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.587686872$ $1.270082799$ 3.447524680 \( \frac{4165509529}{1368900} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 33 a\) , \( -63\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+33a{x}-63$
50700.2-b3 50700.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $0.293843436$ $2.540165599$ 3.447524680 \( \frac{273359449}{9360} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 13 a\) , \( 13\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+13a{x}+13$
50700.2-b4 50700.2-b \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $1.175373745$ $0.635041399$ 3.447524680 \( \frac{12501706118329}{2570490} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 483 a\) , \( -4293\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+483a{x}-4293$
50700.2-c1 50700.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $0.228141728$ $0.216937378$ 3.657534727 \( -\frac{168288035761}{73415764890} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -114 a + 114\) , \( -12978\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-114a+114\right){x}-12978$
50700.2-c2 50700.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/4\Z$ $0.456283456$ $1.735499031$ 3.657534727 \( \frac{371694959}{249600} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(16a-16\right){x}$
50700.2-c3 50700.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.912566913$ $0.867749515$ 3.657534727 \( \frac{30400540561}{15210000} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -64 a + 64\) , \( 112\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-64a+64\right){x}+112$
50700.2-c4 50700.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.456283456$ $0.433874757$ 3.657534727 \( \frac{19948814692561}{231344100} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -564 a + 564\) , \( -4788\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-564a+564\right){x}-4788$
50700.2-c5 50700.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/4\Z$ $1.825133826$ $0.433874757$ 3.657534727 \( \frac{66730743078481}{60937500} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -844 a + 844\) , \( 9940\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-844a+844\right){x}+9940$
50700.2-c6 50700.2-c \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $0.912566913$ $0.216937378$ 3.657534727 \( \frac{81025909800741361}{11088090} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -9014 a + 9014\) , \( -324198\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(-9014a+9014\right){x}-324198$
50700.2-d1 50700.2-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $0.341794385$ $2.438138537$ 3.849042122 \( \frac{6967871}{35100} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -5 a\) , \( -7\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}-5a{x}-7$
50700.2-d2 50700.2-d \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $1$ $\Z/2\Z$ $0.683588771$ $1.219069268$ 3.849042122 \( \frac{10779215329}{1232010} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 45 a\) , \( -127\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+45a{x}-127$
50700.2-e1 50700.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $1.540509251$ 3.557653723 \( -\frac{24137569}{561600} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -6\) , \( 36\bigr] \) ${y}^2+{x}{y}={x}^{3}-6{x}+36$
50700.2-e2 50700.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $0.513503083$ 3.557653723 \( \frac{17394111071}{411937500} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 54\) , \( -960\bigr] \) ${y}^2+{x}{y}={x}^{3}+54{x}-960$
50700.2-e3 50700.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $0.256751541$ 3.557653723 \( \frac{189208196468929}{10860320250} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -1196\) , \( -15210\bigr] \) ${y}^2+{x}{y}={x}^{3}-1196{x}-15210$
50700.2-e4 50700.2-e \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $0.770254625$ 3.557653723 \( \frac{967068262369}{4928040} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -206\) , \( 1116\bigr] \) ${y}^2+{x}{y}={x}^{3}-206{x}+1116$
50700.2-f1 50700.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $0.036238799$ 3.766046509 \( -\frac{16818951115904497561}{1592332281446400} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -53378 a + 53377\) , \( -5124652\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-53378a+53377\right){x}-5124652$
50700.2-f2 50700.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $0.108716398$ 3.766046509 \( \frac{7064514799444439}{4094064000000} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 3997 a - 3998\) , \( 3998\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(3997a-3998\right){x}+3998$
50700.2-f3 50700.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $0.054358199$ 3.766046509 \( \frac{453198971846635561}{261896250564000} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -16003 a + 16002\) , \( 27998\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-16003a+16002\right){x}+27998$
50700.2-f4 50700.2-f \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/6\Z$ $1$ $0.018119399$ 3.766046509 \( \frac{73474353581350183614361}{576510977802240} \) \( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -872578 a + 872577\) , \( -313799212\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-872578a+872577\right){x}-313799212$
50700.2-g1 50700.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/4\Z$ $1$ $0.364863272$ 4.213078166 \( -\frac{2656166199049}{2658140160} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 288 a\) , \( 3092\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+288a{x}+3092$
50700.2-g2 50700.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/2\Z$ $1$ $0.091215818$ 4.213078166 \( \frac{26465989780414729}{10571870144160} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 6208 a\) , \( 104276\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+6208a{x}+104276$
50700.2-g3 50700.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $0.182431636$ 4.213078166 \( \frac{17496824387403529}{6580454400} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 5408 a\) , \( 152596\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+5408a{x}+152596$
50700.2-g4 50700.2-g \(\Q(\sqrt{-3}) \) \( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) $0$ $\Z/2\Z$ $1$ $0.091215818$ 4.213078166 \( \frac{71647584155243142409}{10140000} \) \( \bigl[a\) , \( 0\) , \( 1\) , \( 86528 a\) , \( 9789652\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+86528a{x}+9789652$
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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.