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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
15.1-a1 15.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $16.31232646$ 0.889910366 \( -\frac{721}{75} a - \frac{1}{15} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -a\) , \( -4 a - 7\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-a{x}-4a-7$
15.1-a2 15.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $8.156163233$ 0.889910366 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( 174 a + 260\) , \( 145 a + 374\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(174a+260\right){x}+145a+374$
15.1-a3 15.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.31232646$ 0.889910366 \( -\frac{127041323975657}{1171875} a + \frac{70922198887903}{234375} \) \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -41 a - 75\) , \( 73 a + 131\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-41a-75\right){x}+73a+131$
15.1-a4 15.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.31232646$ 0.889910366 \( \frac{169820651}{5625} a + \frac{28920482}{375} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 27 a - 62\) , \( -106 a + 305\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(27a-62\right){x}-106a+305$
15.1-a5 15.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $8.156163233$ 0.889910366 \( \frac{54809252307092563}{457763671875} a + \frac{17662537283047898}{91552734375} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 382 a - 1057\) , \( -6554 a + 18298\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(382a-1057\right){x}-6554a+18298$
15.1-a6 15.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $4.078081616$ 0.889910366 \( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 67 a - 177\) , \( 271 a - 757\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(67a-177\right){x}+271a-757$
15.1-b1 15.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $19.53039258$ 1.065470266 \( -\frac{721}{75} a - \frac{1}{15} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$
15.1-b2 15.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.220649536$ 1.065470266 \( -\frac{100981119568896026467}{1875} a + \frac{56373474375475478518}{375} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 275 a - 734\) , \( 3747 a - 10492\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(275a-734\right){x}+3747a-10492$
15.1-b3 15.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.882598147$ 1.065470266 \( -\frac{127041323975657}{1171875} a + \frac{70922198887903}{234375} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 15 a - 49\) , \( 66 a - 181\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(15a-49\right){x}+66a-181$
15.1-b4 15.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $19.53039258$ 1.065470266 \( \frac{169820651}{5625} a + \frac{28920482}{375} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -4\) , \( 3 a - 1\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}+3a-1$
15.1-b5 15.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.220649536$ 1.065470266 \( \frac{54809252307092563}{457763671875} a + \frac{17662537283047898}{91552734375} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -5 a - 84\) , \( -3 a - 310\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-5a-84\right){x}-3a-310$
15.1-b6 15.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/8\Z$ $1$ $19.53039258$ 1.065470266 \( \frac{11403943879867}{2025} a + \frac{4085550627187}{405} \) \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -15 a - 39\) , \( 72 a + 135\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a-39\right){x}+72a+135$
15.2-a1 15.2-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $8.156163233$ 0.889910366 \( -\frac{54809252307092563}{457763671875} a + \frac{143121938722332053}{457763671875} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -379 a - 681\) , \( 5873 a + 10526\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-379a-681\right){x}+5873a+10526$
15.2-a2 15.2-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $16.31232646$ 0.889910366 \( \frac{721}{75} a - \frac{242}{25} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( 0\) , \( 3 a - 10\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+3a-10$
15.2-a3 15.2-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $4.078081616$ 0.889910366 \( -\frac{11403943879867}{2025} a + \frac{1178951741326}{75} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -64 a - 116\) , \( -387 a - 694\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-64a-116\right){x}-387a-694$
15.2-a4 15.2-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.31232646$ 0.889910366 \( -\frac{169820651}{5625} a + \frac{603627881}{5625} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -24 a - 41\) , \( 65 a + 116\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-24a-41\right){x}+65a+116$
15.2-a5 15.2-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.31232646$ 0.889910366 \( \frac{127041323975657}{1171875} a + \frac{75856556821286}{390625} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( 40 a - 115\) , \( -74 a + 205\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(40a-115\right){x}-74a+205$
15.2-a6 15.2-a \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $8.156163233$ 0.889910366 \( \frac{100981119568896026467}{1875} a + \frac{180886252308481366123}{1875} \) \( \bigl[1\) , \( a - 1\) , \( a\) , \( -175 a + 435\) , \( -146 a + 520\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-175a+435\right){x}-146a+520$
15.2-b1 15.2-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.220649536$ 1.065470266 \( -\frac{54809252307092563}{457763671875} a + \frac{143121938722332053}{457763671875} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 5 a - 90\) , \( 8 a - 403\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(5a-90\right){x}+8a-403$
15.2-b2 15.2-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/4\Z$ $1$ $19.53039258$ 1.065470266 \( \frac{721}{75} a - \frac{242}{25} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$
15.2-b3 15.2-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/8\Z$ $1$ $19.53039258$ 1.065470266 \( -\frac{11403943879867}{2025} a + \frac{1178951741326}{75} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 15 a - 55\) , \( -57 a + 152\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a-55\right){x}-57a+152$
15.2-b4 15.2-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $19.53039258$ 1.065470266 \( -\frac{169820651}{5625} a + \frac{603627881}{5625} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -3 a - 3\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}-5{x}-3a-3$
15.2-b5 15.2-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $4.882598147$ 1.065470266 \( \frac{127041323975657}{1171875} a + \frac{75856556821286}{390625} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -15 a - 35\) , \( -81 a - 150\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-15a-35\right){x}-81a-150$
15.2-b6 15.2-b \(\Q(\sqrt{21}) \) \( 3 \cdot 5 \) $0$ $\Z/2\Z$ $1$ $1.220649536$ 1.065470266 \( \frac{100981119568896026467}{1875} a + \frac{180886252308481366123}{1875} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -275 a - 460\) , \( -4022 a - 7205\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-275a-460\right){x}-4022a-7205$
16.1-a1 16.1-a \(\Q(\sqrt{21}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-3$ $1$ $17.69503190$ 0.965343132 \( 0 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 2\) , \( -2\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+2\right){x}-2$
16.1-a2 16.1-a \(\Q(\sqrt{21}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-3$ $1$ $17.69503190$ 0.965343132 \( 0 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+2\right){x}$
16.1-a3 16.1-a \(\Q(\sqrt{21}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-12$ $1$ $17.69503190$ 0.965343132 \( 54000 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 13\) , \( 11 a - 31\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(6a-13\right){x}+11a-31$
16.1-a4 16.1-a \(\Q(\sqrt{21}) \) \( 2^{4} \) $0$ $\Z/2\Z$ $-12$ $1$ $17.69503190$ 0.965343132 \( 54000 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 8\) , \( -16 a - 28\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-4a-8\right){x}-16a-28$
17.1-a1 17.1-a \(\Q(\sqrt{21}) \) \( 17 \) $0$ $\Z/3\Z$ $1$ $45.16448385$ 1.095077597 \( \frac{20811}{17} a - \frac{19591}{17} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -7\) , \( -2 a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}-7{x}-2a+2$
17.1-a2 17.1-a \(\Q(\sqrt{21}) \) \( 17 \) $0$ $\mathsf{trivial}$ $1$ $5.018275983$ 1.095077597 \( \frac{2723256379739}{4913} a + \frac{4878142779916}{4913} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -15 a + 33\) , \( 10 a - 33\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-15a+33\right){x}+10a-33$
17.1-b1 17.1-b \(\Q(\sqrt{21}) \) \( 17 \) $1$ $\mathsf{trivial}$ $0.092314733$ $19.62917645$ 0.790848774 \( \frac{20811}{17} a - \frac{19591}{17} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-a+1\right){x}$
17.1-b2 17.1-b \(\Q(\sqrt{21}) \) \( 17 \) $1$ $\Z/3\Z$ $0.276944199$ $19.62917645$ 0.790848774 \( \frac{2723256379739}{4913} a + \frac{4878142779916}{4913} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -11 a - 14\) , \( 26 a + 50\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-11a-14\right){x}+26a+50$
17.2-a1 17.2-a \(\Q(\sqrt{21}) \) \( 17 \) $0$ $\Z/3\Z$ $1$ $45.16448385$ 1.095077597 \( -\frac{20811}{17} a + \frac{1220}{17} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -2 a - 5\) , \( a + 1\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-2a-5\right){x}+a+1$
17.2-a2 17.2-a \(\Q(\sqrt{21}) \) \( 17 \) $0$ $\mathsf{trivial}$ $1$ $5.018275983$ 1.095077597 \( -\frac{2723256379739}{4913} a + \frac{7601399159655}{4913} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 13 a + 20\) , \( -11 a - 22\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(13a+20\right){x}-11a-22$
17.2-b1 17.2-b \(\Q(\sqrt{21}) \) \( 17 \) $1$ $\mathsf{trivial}$ $0.092314733$ $19.62917645$ 0.790848774 \( -\frac{20811}{17} a + \frac{1220}{17} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}$
17.2-b2 17.2-b \(\Q(\sqrt{21}) \) \( 17 \) $1$ $\Z/3\Z$ $0.276944199$ $19.62917645$ 0.790848774 \( -\frac{2723256379739}{4913} a + \frac{7601399159655}{4913} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 10 a - 25\) , \( -26 a + 76\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(10a-25\right){x}-26a+76$
21.1-a1 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.651881942$ 0.796905972 \( -\frac{4354703137}{17294403} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 170 a - 477\) , \( -5038 a + 14062\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(170a-477\right){x}-5038a+14062$
21.1-a2 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $14.60752776$ 0.796905972 \( \frac{103823}{63} \) \( \bigl[a\) , \( 1\) , \( a\) , \( -5 a + 13\) , \( -5 a + 13\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-5a+13\right){x}-5a+13$
21.1-a3 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $14.60752776$ 0.796905972 \( \frac{7189057}{3969} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 20 a - 57\) , \( -4 a + 10\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(20a-57\right){x}-4a+10$
21.1-a4 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $0$ $\Z/2\Z$ $1$ $3.651881942$ 0.796905972 \( \frac{6570725617}{45927} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 195 a - 547\) , \( 2355 a - 6577\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(195a-547\right){x}+2355a-6577$
21.1-a5 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $14.60752776$ 0.796905972 \( \frac{13027640977}{21609} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 245 a - 687\) , \( -3019 a + 8425\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(245a-687\right){x}-3019a+8425$
21.1-a6 21.1-a \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $0$ $\Z/4\Z$ $1$ $14.60752776$ 0.796905972 \( \frac{53297461115137}{147} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 3920 a - 10977\) , \( -200440 a + 559528\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3920a-10977\right){x}-200440a+559528$
21.1-b1 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $2.638508823$ $0.814020435$ 0.937376813 \( -\frac{4354703137}{17294403} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \) ${y}^2+{x}{y}={x}^{3}-34{x}-217$
21.1-b2 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/8\Z$ $1.319254411$ $13.02432697$ 0.937376813 \( \frac{103823}{63} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}$
21.1-b3 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $0.659627205$ $13.02432697$ 0.937376813 \( \frac{7189057}{3969} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^{3}-4{x}-1$
21.1-b4 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/8\Z$ $0.329813602$ $13.02432697$ 0.937376813 \( \frac{6570725617}{45927} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \) ${y}^2+{x}{y}={x}^{3}-39{x}+90$
21.1-b5 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $1.319254411$ $3.256081743$ 0.937376813 \( \frac{13027640977}{21609} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \) ${y}^2+{x}{y}={x}^{3}-49{x}-136$
21.1-b6 21.1-b \(\Q(\sqrt{21}) \) \( 3 \cdot 7 \) $1$ $\Z/2\Z$ $2.638508823$ $0.814020435$ 0.937376813 \( \frac{53297461115137}{147} \) \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \) ${y}^2+{x}{y}={x}^{3}-784{x}-8515$
25.1-a1 25.1-a \(\Q(\sqrt{21}) \) \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.961531894$ 1.082695022 \( -\frac{359104782699}{244140625} a - \frac{52148361654}{48828125} \) \( \bigl[a\) , \( a\) , \( a + 1\) , \( -26 a - 43\) , \( 84 a + 148\bigr] \) ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-26a-43\right){x}+84a+148$
25.1-a2 25.1-a \(\Q(\sqrt{21}) \) \( 5^{2} \) $0$ $\Z/2\Z$ $1$ $4.961531894$ 1.082695022 \( \frac{359104782699}{244140625} a - \frac{619846590969}{244140625} \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 29 a - 66\) , \( -125 a + 369\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(29a-66\right){x}-125a+369$
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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.