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Results (20 matches)

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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
14400.1-a1 14400.1-a \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $0.134291398$ $1.081426142$ 2.634737040 \( -\frac{343139}{6075} a + \frac{1391954}{18225} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -2 a + 16\) , \( 17 a + 90\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+16\right){x}+17a+90$
14400.1-a2 14400.1-a \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $0.268582796$ $2.162852284$ 2.634737040 \( -\frac{6507349}{135} a + \frac{3273806}{135} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 13 a + 6\) , \( -8 a + 48\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(13a+6\right){x}-8a+48$
14400.1-b1 14400.1-b \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.261832364$ 1.907711219 \( \frac{73891081}{1875} a - \frac{37962002}{1875} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 45 a - 32\) , \( 129 a + 17\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(45a-32\right){x}+129a+17$
14400.1-b2 14400.1-b \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.523664729$ 1.907711219 \( \frac{5159}{75} a - \frac{3598}{225} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -2\) , \( 3 a + 5\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}-2{x}+3a+5$
14400.1-b3 14400.1-b \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $2.523664729$ 1.907711219 \( -\frac{819929}{135} a + \frac{6035234}{405} \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 5 a + 6\) , \( -4 a + 8\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+6\right){x}-4a+8$
14400.1-b4 14400.1-b \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $2.523664729$ 1.907711219 \( -\frac{1997369}{15} a + \frac{2728978}{15} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 13 a - 12\) , \( 17 a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(13a-12\right){x}+17a+1$
14400.1-c1 14400.1-c \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $0.592420197$ 0.895655150 \( \frac{427962719}{270000} a - \frac{4540203359}{810000} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -82 a + 171\) , \( -355 a - 573\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-82a+171\right){x}-355a-573$
14400.1-c2 14400.1-c \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.184840394$ 0.895655150 \( \frac{283009199}{327680} a - \frac{2474048159}{983040} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( -22 a - 8\) , \( -69 a + 46\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(-22a-8\right){x}-69a+46$
14400.1-c3 14400.1-c \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $1.184840394$ 0.895655150 \( -\frac{26440799}{19200} a - \frac{112620977}{57600} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -27 a + 1\) , \( -86 a + 85\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-27a+1\right){x}-86a+85$
14400.1-c4 14400.1-c \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.184840394$ 0.895655150 \( \frac{746269231}{80} a + \frac{746269649}{240} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( 25 a - 168\) , \( -262 a + 891\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-168\right){x}-262a+891$
14400.1-d1 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $15.27600809$ $0.197609980$ 4.563832806 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -550 a - 221\) , \( -14407 a + 5499\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-550a-221\right){x}-14407a+5499$
14400.1-d2 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $0.954750506$ $3.161759683$ 4.563832806 \( -\frac{1}{15} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -1\) , \( 3 a - 1\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}-{x}+3a-1$
14400.1-d3 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $1.909501012$ $0.395219960$ 4.563832806 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 175 a + 69\) , \( -648 a + 97\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(175a+69\right){x}-648a+97$
14400.1-d4 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $3.819002024$ $0.790439920$ 4.563832806 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -50 a - 21\) , \( -117 a + 79\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-50a-21\right){x}-117a+79$
14400.1-d5 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.909501012$ $1.580879841$ 4.563832806 \( \frac{13997521}{225} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -25 a - 11\) , \( 62 a - 3\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-25a-11\right){x}+62a-3$
14400.1-d6 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $7.638004048$ $0.395219960$ 4.563832806 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -675 a - 271\) , \( -10542 a + 4229\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-675a-271\right){x}-10542a+4229$
14400.1-d7 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $3.819002024$ $0.790439920$ 4.563832806 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -400 a - 161\) , \( 4517 a - 1293\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-400a-161\right){x}+4517a-1293$
14400.1-d8 14400.1-d \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $1$ $\Z/2\Z$ $15.27600809$ $0.197609980$ 4.563832806 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -10800 a - 4321\) , \( -661377 a + 241559\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-10800a-4321\right){x}-661377a+241559$
14400.1-e1 14400.1-e \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $1.962573393$ 2.967132073 \( \frac{803941}{75} a - \frac{1619806}{225} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -15 a + 12\) , \( -12 a + 31\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-15a+12\right){x}-12a+31$
14400.1-e2 14400.1-e \(\Q(\sqrt{-7}) \) \( 2^{6} \cdot 3^{2} \cdot 5^{2} \) $0$ $\Z/2\Z$ $1$ $3.925146786$ 2.967132073 \( -\frac{349}{15} a - \frac{4354}{15} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2\) , \( -2 a + 3\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+2{x}-2a+3$
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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.