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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
1.1-a1 1.1-a \(\Q(\sqrt{38}) \) \( 1 \) $0$ $\Z/2\Z$ $-8$ $1$ $50.75994773$ 1.029293857 \( 8000 \) \( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -5 a + 15\) , \( -5 a + 21\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+15\right){x}-5a+21$
1.1-a2 1.1-a \(\Q(\sqrt{38}) \) \( 1 \) $0$ $\Z/2\Z$ $-8$ $1$ $50.75994773$ 1.029293857 \( 8000 \) \( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 4 a + 15\) , \( 4 a + 21\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+15\right){x}+4a+21$
16.1-a1 16.1-a \(\Q(\sqrt{38}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-8$ $1$ $25.37997386$ 0.514646928 \( 8000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( -10 a - 49\) , \( 57 a + 360\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(-10a-49\right){x}+57a+360$
16.1-a2 16.1-a \(\Q(\sqrt{38}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-8$ $1$ $25.37997386$ 0.514646928 \( 8000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 10 a - 49\) , \( -57 a + 360\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(10a-49\right){x}-57a+360$
19.1-a1 19.1-a \(\Q(\sqrt{38}) \) \( 19 \) $0$ $\mathsf{trivial}$ $1$ $6.315973634$ 1.024586218 \( \frac{10648000}{6859} \) \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 34 a + 219\) , \( 232 a + 1433\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a+219\right){x}+232a+1433$
19.1-b1 19.1-b \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\mathsf{trivial}$ $41.68961490$ $0.205438503$ 2.778740071 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -769\) , \( -8470\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$
19.1-b2 19.1-b \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\Z/3\Z$ $13.89653830$ $1.848946532$ 2.778740071 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -9\) , \( -15\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$
19.1-b3 19.1-b \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\Z/3\Z$ $4.632179434$ $16.64051879$ 2.778740071 \( \frac{32768}{19} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+{x}$
19.1-c1 19.1-c \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\mathsf{trivial}$ $0.731231101$ $12.79541874$ 3.035619650 \( -\frac{2299968}{19} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( -17 a - 65\) , \( -149 a - 876\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-17a-65\right){x}-149a-876$
19.1-d1 19.1-d \(\Q(\sqrt{38}) \) \( 19 \) $0$ $\mathsf{trivial}$ $1$ $6.315973634$ 1.024586218 \( \frac{10648000}{6859} \) \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -35 a + 219\) , \( -232 a + 1433\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-35a+219\right){x}-232a+1433$
19.1-e1 19.1-e \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\mathsf{trivial}$ $0.595904332$ $17.03289160$ 3.293086381 \( -\frac{50357871050752}{19} \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 341584 a - 2105665\) , \( -269922166 a + 1663911967\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(341584a-2105665\right){x}-269922166a+1663911967$
19.1-e2 19.1-e \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\mathsf{trivial}$ $0.198634777$ $17.03289160$ 3.293086381 \( -\frac{89915392}{6859} \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 4144 a - 25545\) , \( -384936 a + 2372892\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4144a-25545\right){x}-384936a+2372892$
19.1-e3 19.1-e \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\mathsf{trivial}$ $0.595904332$ $17.03289160$ 3.293086381 \( \frac{32768}{19} \) \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 296 a + 1825\) , \( 205 a + 1257\bigr] \) ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(296a+1825\right){x}+205a+1257$
19.1-f1 19.1-f \(\Q(\sqrt{38}) \) \( 19 \) $1$ $\mathsf{trivial}$ $0.731231101$ $12.79541874$ 3.035619650 \( -\frac{2299968}{19} \) \( \bigl[a\) , \( 1\) , \( 1\) , \( 16 a - 65\) , \( 149 a - 876\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(16a-65\right){x}+149a-876$
22.1-a1 22.1-a \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $2.087525364$ 3.047771981 \( \frac{5339530805}{10648} a - \frac{32950208549}{10648} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 601 a - 3690\) , \( 22656 a - 139650\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(601a-3690\right){x}+22656a-139650$
22.1-b1 22.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $1.110557261$ 4.053513987 \( -\frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 859 a - 5176\) , \( 33615 a - 206970\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(859a-5176\right){x}+33615a-206970$
22.1-b2 22.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $0$ $\Z/5\Z$ $1$ $27.76393154$ 4.053513987 \( -\frac{21141}{88} a + \frac{33588}{11} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 14 a + 34\) , \( 12 a + 180\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(14a+34\right){x}+12a+180$
22.1-c1 22.1-c \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $0.093479625$ $27.42927522$ 2.495690633 \( \frac{5339530805}{10648} a - \frac{32950208549}{10648} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -3 a - 7\) , \( 15 a + 87\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-7\right){x}+15a+87$
22.1-d1 22.1-d \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $0.175606115$ $19.56167963$ 2.786275040 \( -\frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -470 a - 2899\) , \( 13901 a + 85693\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-470a-2899\right){x}+13901a+85693$
22.1-d2 22.1-d \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $0.878030577$ $19.56167963$ 2.786275040 \( -\frac{21141}{88} a + \frac{33588}{11} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 5 a + 31\) , \( -6 a - 37\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(5a+31\right){x}-6a-37$
22.2-a1 22.2-a \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $2.087525364$ 3.047771981 \( -\frac{5339530805}{10648} a - \frac{32950208549}{10648} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -601 a - 3690\) , \( -22656 a - 139650\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-601a-3690\right){x}-22656a-139650$
22.2-b1 22.2-b \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $0$ $\Z/5\Z$ $1$ $27.76393154$ 4.053513987 \( \frac{21141}{88} a + \frac{33588}{11} \) \( \bigl[a + 1\) , \( a\) , \( a\) , \( 5 a + 15\) , \( 3 a + 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+15\right){x}+3a+9$
22.2-b2 22.2-b \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $1.110557261$ 4.053513987 \( \frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) \( \bigl[a + 1\) , \( a\) , \( a\) , \( -840 a - 5195\) , \( -38810 a - 239251\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-840a-5195\right){x}-38810a-239251$
22.2-c1 22.2-c \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $0.093479625$ $27.42927522$ 2.495690633 \( -\frac{5339530805}{10648} a - \frac{32950208549}{10648} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( 2 a - 7\) , \( -15 a + 87\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-7\right){x}-15a+87$
22.2-d1 22.2-d \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $0.878030577$ $19.56167963$ 2.786275040 \( \frac{21141}{88} a + \frac{33588}{11} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -5 a + 31\) , \( 6 a - 37\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-5a+31\right){x}+6a-37$
22.2-d2 22.2-d \(\Q(\sqrt{38}) \) \( 2 \cdot 11 \) $1$ $\mathsf{trivial}$ $0.175606115$ $19.56167963$ 2.786275040 \( \frac{689814863492301}{322102} a + \frac{2125836434628648}{161051} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 470 a - 2899\) , \( -13901 a + 85693\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(470a-2899\right){x}-13901a+85693$
26.1-a1 26.1-a \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $0.405491309$ $10.82199744$ 5.694913962 \( \frac{426533}{208} a - \frac{2186819}{208} \) \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -a + 6\) , \( a + 5\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+6\right){x}+a+5$
26.1-b1 26.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $0.225757248$ $38.42654873$ 5.629129986 \( \frac{37576645441}{52} a + \frac{231628356997}{52} \) \( \bigl[1\) , \( -a\) , \( 0\) , \( 106 a - 642\) , \( -1260 a + 7760\bigr] \) ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(106a-642\right){x}-1260a+7760$
26.1-c1 26.1-c \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $3.016839248$ $2.728415556$ 2.670551047 \( \frac{37576645441}{52} a + \frac{231628356997}{52} \) \( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -106 a - 607\) , \( -1614 a - 9889\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-106a-607\right){x}-1614a-9889$
26.1-d1 26.1-d \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $0.249960593$ $30.75820572$ 2.494426677 \( \frac{426533}{208} a - \frac{2186819}{208} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 80 a - 504\) , \( -729 a + 4492\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(80a-504\right){x}-729a+4492$
26.2-a1 26.2-a \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $0.405491309$ $10.82199744$ 5.694913962 \( -\frac{426533}{208} a - \frac{2186819}{208} \) \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 6\) , \( -2 a + 5\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+6{x}-2a+5$
26.2-b1 26.2-b \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $0.225757248$ $38.42654873$ 5.629129986 \( -\frac{37576645441}{52} a + \frac{231628356997}{52} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -106 a - 642\) , \( 1260 a + 7760\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-106a-642\right){x}+1260a+7760$
26.2-c1 26.2-c \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $3.016839248$ $2.728415556$ 2.670551047 \( -\frac{37576645441}{52} a + \frac{231628356997}{52} \) \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 106 a - 607\) , \( 1614 a - 9889\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(106a-607\right){x}+1614a-9889$
26.2-d1 26.2-d \(\Q(\sqrt{38}) \) \( 2 \cdot 13 \) $1$ $\mathsf{trivial}$ $0.249960593$ $30.75820572$ 2.494426677 \( -\frac{426533}{208} a - \frac{2186819}{208} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -82 a - 504\) , \( 728 a + 4492\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-82a-504\right){x}+728a+4492$
32.1-a1 32.1-a \(\Q(\sqrt{38}) \) \( 2^{5} \) $0$ $\mathsf{trivial}$ $1$ $12.57159272$ 2.039381637 \( -8000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 11\) , \( -a\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+11{x}-a$
32.1-b1 32.1-b \(\Q(\sqrt{38}) \) \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.869038602$ $12.57159272$ 3.544602734 \( -8000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( -740 a - 4549\) , \( 28481 a + 175560\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(-740a-4549\right){x}+28481a+175560$
32.1-c1 32.1-c \(\Q(\sqrt{38}) \) \( 2^{5} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $7.228619307$ $27.50074327$ 4.031048281 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \) ${y}^2={x}^{3}-{x}$
32.1-c2 32.1-c \(\Q(\sqrt{38}) \) \( 2^{5} \) $1$ $\Z/4\Z$ $-4$ $14.45723861$ $13.75037163$ 4.031048281 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 444 a + 2737\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(444a+2737\right){x}$
32.1-c3 32.1-c \(\Q(\sqrt{38}) \) \( 2^{5} \) $1$ $\Z/2\Z$ $-16$ $3.614309653$ $13.75037163$ 4.031048281 \( 287496 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -1221 a - 7509\) , \( -61761 a - 380687\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1221a-7509\right){x}-61761a-380687$
32.1-c4 32.1-c \(\Q(\sqrt{38}) \) \( 2^{5} \) $1$ $\Z/4\Z$ $-16$ $3.614309653$ $55.00148654$ 4.031048281 \( 287496 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -1221 a - 7490\) , \( 53214 a + 328076\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-1221a-7490\right){x}+53214a+328076$
32.1-d1 32.1-d \(\Q(\sqrt{38}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $-4$ $1$ $13.75037163$ 0.557651206 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^{3}+{x}$
32.1-d2 32.1-d \(\Q(\sqrt{38}) \) \( 2^{5} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ $1$ $27.50074327$ 0.557651206 \( 1728 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -444 a - 2737\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-444a-2737\right){x}$
32.1-d3 32.1-d \(\Q(\sqrt{38}) \) \( 2^{5} \) $0$ $\Z/2\Z$ $-16$ $1$ $13.75037163$ 0.557651206 \( 287496 \) \( \bigl[a\) , \( 1\) , \( a\) , \( 15\) , \( 22\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+15{x}+22$
32.1-d4 32.1-d \(\Q(\sqrt{38}) \) \( 2^{5} \) $0$ $\Z/4\Z$ $-16$ $1$ $55.00148654$ 0.557651206 \( 287496 \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 34\) , \( 35\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+34{x}+35$
32.1-e1 32.1-e \(\Q(\sqrt{38}) \) \( 2^{5} \) $0$ $\mathsf{trivial}$ $1$ $12.57159272$ 2.039381637 \( -8000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 11\) , \( a\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+11{x}+a$
32.1-f1 32.1-f \(\Q(\sqrt{38}) \) \( 2^{5} \) $1$ $\mathsf{trivial}$ $0.869038602$ $12.57159272$ 3.544602734 \( -8000 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 740 a - 4549\) , \( -28481 a + 175560\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(740a-4549\right){x}-28481a+175560$
34.1-a1 34.1-a \(\Q(\sqrt{38}) \) \( 2 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $43.84367238$ 1.778095710 \( -\frac{30286}{17} a + \frac{933185}{68} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( 299 a - 1832\) , \( -6106 a + 37632\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(299a-1832\right){x}-6106a+37632$
34.1-a2 34.1-a \(\Q(\sqrt{38}) \) \( 2 \cdot 17 \) $0$ $\Z/2\Z$ $1$ $21.92183619$ 1.778095710 \( -\frac{13448510910}{289} a + \frac{165825143353}{578} \) \( \bigl[1\) , \( -a\) , \( 1\) , \( 4739 a - 29202\) , \( -430790 a + 2655560\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4739a-29202\right){x}-430790a+2655560$
34.1-b1 34.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 17 \) $1$ $\Z/2\Z$ $1.703437555$ $22.75725313$ 6.288604174 \( -\frac{30286}{17} a + \frac{933185}{68} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a + 8\) , \( -5 a + 21\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+8\right){x}-5a+21$
34.1-b2 34.1-b \(\Q(\sqrt{38}) \) \( 2 \cdot 17 \) $1$ $\Z/2\Z$ $3.406875110$ $11.37862656$ 6.288604174 \( -\frac{13448510910}{289} a + \frac{165825143353}{578} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 2\) , \( -a - 7\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-2\right){x}-a-7$
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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.