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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
9.1-a1 9.1-a \(\Q(\sqrt{3}) \) \( 3^{2} \) $0$ $\Z/2\Z$ $-36$ $1$ $3.283496869$ 0.473931950 \( -44330496 a + 76771008 \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 25 a - 45\) , \( 72 a - 127\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-45\right){x}+72a-127$
9.1-a2 9.1-a \(\Q(\sqrt{3}) \) \( 3^{2} \) $0$ $\Z/6\Z$ $-36$ $1$ $29.55147182$ 0.473931950 \( -44330496 a + 76771008 \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 25 a - 45\) , \( -117 a + 202\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(25a-45\right){x}-117a+202$
9.1-a3 9.1-a \(\Q(\sqrt{3}) \) \( 3^{2} \) $0$ $\Z/6\Z$ $-4$ $1$ $29.55147182$ 0.473931950 \( 1728 \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}$
9.1-a4 9.1-a \(\Q(\sqrt{3}) \) \( 3^{2} \) $0$ $\Z/6\Z$ $-4$ $1$ $29.55147182$ 0.473931950 \( 1728 \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -7 a + 13\) , \( 6 a - 10\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-7a+13\right){x}+6a-10$
9.1-a5 9.1-a \(\Q(\sqrt{3}) \) \( 3^{2} \) $0$ $\Z/2\Z$ $-36$ $1$ $3.283496869$ 0.473931950 \( 44330496 a + 76771008 \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 88 a - 152\) , \( 564 a - 977\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(88a-152\right){x}+564a-977$
9.1-a6 9.1-a \(\Q(\sqrt{3}) \) \( 3^{2} \) $0$ $\Z/6\Z$ $-36$ $1$ $29.55147182$ 0.473931950 \( 44330496 a + 76771008 \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 88 a - 152\) , \( -717 a + 1242\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(88a-152\right){x}-717a+1242$
16.1-a1 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/4\Z$ $-3$ $1$ $17.69503190$ 0.638514464 \( 0 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 1\) , \( -3 a - 5\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+{x}-3a-5$
16.1-a2 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/4\Z$ $-3$ $1$ $17.69503190$ 0.638514464 \( 0 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 1\) , \( 3 a + 5\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+{x}+3a+5$
16.1-a3 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-48$ $1$ $8.847515954$ 0.638514464 \( -818626500 a + 1417905000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 4 a - 13\) , \( 11 a - 21\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(4a-13\right){x}+11a-21$
16.1-a4 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/4\Z$ $-48$ $1$ $35.39006381$ 0.638514464 \( -818626500 a + 1417905000 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 4 a - 13\) , \( -12 a + 19\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4a-13\right){x}-12a+19$
16.1-a5 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $1$ $35.39006381$ 0.638514464 \( 54000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 3\) , \( -1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-3\right){x}-1$
16.1-a6 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $-12$ $1$ $35.39006381$ 0.638514464 \( 54000 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -a - 3\) , \( -a - 1\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-a-3\right){x}-a-1$
16.1-a7 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-48$ $1$ $8.847515954$ 0.638514464 \( 818626500 a + 1417905000 \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -6 a - 13\) , \( -12 a - 21\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-6a-13\right){x}-12a-21$
16.1-a8 16.1-a \(\Q(\sqrt{3}) \) \( 2^{4} \) $0$ $\Z/4\Z$ $-48$ $1$ $35.39006381$ 0.638514464 \( 818626500 a + 1417905000 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -6 a - 13\) , \( 11 a + 19\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-6a-13\right){x}+11a+19$
22.1-a1 22.1-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/3\Z$ $1$ $19.48623858$ 0.625021394 \( -\frac{3800943658260597}{322102} a - \frac{6583595299744607}{322102} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( 14261 a - 24701\) , \( -1229141 a + 2128933\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(14261a-24701\right){x}-1229141a+2128933$
22.1-a2 22.1-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $2.165137620$ 0.625021394 \( -\frac{14621235235888115443}{16708992677662604} a - \frac{20728089694692551503}{16708992677662604} \) \( \bigl[1\) , \( a\) , \( a + 1\) , \( -23694 a + 41039\) , \( -5992615 a + 10379512\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-23694a+41039\right){x}-5992615a+10379512$
22.1-a3 22.1-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $2.165137620$ 0.625021394 \( \frac{7452136447}{340736} a - \frac{12920117437}{340736} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 18 a - 33\) , \( 83 a - 145\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(18a-33\right){x}+83a-145$
22.1-a4 22.1-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/3\Z$ $1$ $19.48623858$ 0.625021394 \( -\frac{26727}{88} a + \frac{49507}{88} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a + 2\) , \( -a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-2a+2\right){x}-a+1$
22.1-b1 22.1-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $0.597897022$ 0.862990016 \( -\frac{3800943658260597}{322102} a - \frac{6583595299744607}{322102} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( 14261 a - 24702\) , \( 1229140 a - 2128935\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(14261a-24702\right){x}+1229140a-2128935$
22.1-b2 22.1-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/3\Z$ $1$ $0.597897022$ 0.862990016 \( -\frac{14621235235888115443}{16708992677662604} a - \frac{20728089694692551503}{16708992677662604} \) \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -23694 a + 41038\) , \( 5992614 a - 10379514\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23694a+41038\right){x}+5992614a-10379514$
22.1-b3 22.1-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/15\Z$ $1$ $14.94742555$ 0.862990016 \( \frac{7452136447}{340736} a - \frac{12920117437}{340736} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 20 a - 32\) , \( -64 a + 112\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(20a-32\right){x}-64a+112$
22.1-b4 22.1-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/5\Z$ $1$ $14.94742555$ 0.862990016 \( -\frac{26727}{88} a + \frac{49507}{88} \) \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+3{x}+1$
22.2-a1 22.2-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/3\Z$ $1$ $19.48623858$ 0.625021394 \( \frac{3800943658260597}{322102} a - \frac{6583595299744607}{322102} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1813 a - 3142\) , \( -55168 a + 95554\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(1813a-3142\right){x}-55168a+95554$
22.2-a2 22.2-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $2.165137620$ 0.625021394 \( -\frac{7452136447}{340736} a - \frac{12920117437}{340736} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -18 a - 33\) , \( -83 a - 145\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-18a-33\right){x}-83a-145$
22.2-a3 22.2-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $2.165137620$ 0.625021394 \( \frac{14621235235888115443}{16708992677662604} a - \frac{20728089694692551503}{16708992677662604} \) \( \bigl[1\) , \( 0\) , \( 1\) , \( 1688 a - 2922\) , \( -63194 a + 109458\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+\left(1688a-2922\right){x}-63194a+109458$
22.2-a4 22.2-a \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/3\Z$ $1$ $19.48623858$ 0.625021394 \( \frac{26727}{88} a + \frac{49507}{88} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(2a+2\right){x}+a+1$
22.2-b1 22.2-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\mathsf{trivial}$ $1$ $0.597897022$ 0.862990016 \( \frac{3800943658260597}{322102} a - \frac{6583595299744607}{322102} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 1813 a - 3143\) , \( 55168 a - 95555\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1813a-3143\right){x}+55168a-95555$
22.2-b2 22.2-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/15\Z$ $1$ $14.94742555$ 0.862990016 \( -\frac{7452136447}{340736} a - \frac{12920117437}{340736} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -20 a - 32\) , \( 64 a + 112\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-20a-32\right){x}+64a+112$
22.2-b3 22.2-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/3\Z$ $1$ $0.597897022$ 0.862990016 \( \frac{14621235235888115443}{16708992677662604} a - \frac{20728089694692551503}{16708992677662604} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 1688 a - 2923\) , \( 63194 a - 109459\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(1688a-2923\right){x}+63194a-109459$
22.2-b4 22.2-b \(\Q(\sqrt{3}) \) \( 2 \cdot 11 \) $0$ $\Z/5\Z$ $1$ $14.94742555$ 0.862990016 \( \frac{26727}{88} a + \frac{49507}{88} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 3\) , \( 1\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+3{x}+1$
24.1-a1 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $18.60223895$ 0.671250479 \( -\frac{79558124472974}{3} a + 45932904578280 \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 1035 a - 1791\) , \( -23450 a + 40617\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(1035a-1791\right){x}-23450a+40617$
24.1-a2 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $2.325279868$ 0.671250479 \( \frac{207646}{6561} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -15 a + 29\) , \( 322 a - 557\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(-15a+29\right){x}+322a-557$
24.1-a3 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/8\Z$ $1$ $18.60223895$ 0.671250479 \( \frac{2048}{3} \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -38 a + 66\) , \( -168 a + 291\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-38a+66\right){x}-168a+291$
24.1-a4 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $37.20447790$ 0.671250479 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 5 a - 6\) , \( -3 a + 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(5a-6\right){x}-3a+6$
24.1-a5 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $9.301119475$ 0.671250479 \( \frac{1556068}{81} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 25 a - 41\) , \( 92 a - 159\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(25a-41\right){x}+92a-159$
24.1-a6 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $37.20447790$ 0.671250479 \( \frac{28756228}{3} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 65 a - 111\) , \( -348 a + 603\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(65a-111\right){x}-348a+603$
24.1-a7 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $2.325279868$ 0.671250479 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 385 a - 671\) , \( 5582 a - 9681\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(385a-671\right){x}+5582a-9681$
24.1-a8 24.1-a \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $18.60223895$ 0.671250479 \( \frac{79558124472974}{3} a + 45932904578280 \) \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 55 a - 111\) , \( -406 a + 717\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+{x}^{2}+\left(55a-111\right){x}-406a+717$
24.1-b1 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $1.420877129$ 0.820343793 \( -\frac{79558124472974}{3} a + 45932904578280 \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1033 a - 1794\) , \( 24484 a - 42410\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(1033a-1794\right){x}+24484a-42410$
24.1-b2 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/8\Z$ $1$ $5.683508517$ 0.820343793 \( \frac{207646}{6561} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -17 a + 26\) , \( -338 a + 584\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-17a+26\right){x}-338a+584$
24.1-b3 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/4\Z$ $1$ $11.36701703$ 0.820343793 \( \frac{2048}{3} \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -38 a + 66\) , \( 168 a - 291\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}+\left(-38a+66\right){x}+168a-291$
24.1-b4 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $22.73403407$ 0.820343793 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 3 a - 9\) , \( 7 a - 14\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(3a-9\right){x}+7a-14$
24.1-b5 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/8\Z$ $1$ $22.73403407$ 0.820343793 \( \frac{1556068}{81} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 23 a - 44\) , \( -68 a + 116\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(23a-44\right){x}-68a+116$
24.1-b6 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $5.683508517$ 0.820343793 \( \frac{28756228}{3} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 63 a - 114\) , \( 412 a - 716\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(63a-114\right){x}+412a-716$
24.1-b7 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/8\Z$ $1$ $22.73403407$ 0.820343793 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 383 a - 674\) , \( -5198 a + 9008\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(383a-674\right){x}-5198a+9008$
24.1-b8 24.1-b \(\Q(\sqrt{3}) \) \( 2^{3} \cdot 3 \) $0$ $\Z/2\Z$ $1$ $1.420877129$ 0.820343793 \( \frac{79558124472974}{3} a + 45932904578280 \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 53 a - 114\) , \( 460 a - 830\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(53a-114\right){x}+460a-830$
33.1-a1 33.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $8.787380279$ 1.268349092 \( -\frac{1081911102879025664}{77812273803} a - \frac{605477717460973120}{25937424601} \) \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 22986 a - 39809\) , \( -2497992 a + 4326651\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(22986a-39809\right){x}-2497992a+4326651$
33.1-a2 33.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $8.787380279$ 1.268349092 \( -\frac{2084278784}{3267} a + \frac{1204895680}{1089} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 6 a - 8\) , \( 12 a - 19\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(6a-8\right){x}+12a-19$
33.1-a3 33.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $8.787380279$ 1.268349092 \( \frac{2291200}{2673} a + \frac{1654208}{2673} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 15 a - 28\) , \( 96 a - 167\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15a-28\right){x}+96a-167$
33.1-a4 33.1-a \(\Q(\sqrt{3}) \) \( 3 \cdot 11 \) $0$ $\Z/2\Z$ $1$ $8.787380279$ 1.268349092 \( \frac{313724549420617141760}{483153} a + \frac{543386859178009155008}{483153} \) \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 57891 a - 100269\) , \( -25338895 a + 43888254\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(57891a-100269\right){x}-25338895a+43888254$
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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.