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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
15.1-a1 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558925428$ 0.288627850 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-110{x}-880$
15.1-a2 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $8.942806850$ 0.288627850 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2$
15.1-a3 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $1.117850856$ 0.288627850 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2+35{x}-28$
15.1-a4 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.235701712$ 0.288627850 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-10{x}-10$
15.1-a5 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $8.942806850$ 0.288627850 \( \frac{46942}{15} a + \frac{725689}{15} \) \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 3\) , \( -a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3-{x}^2+3{x}-a+2$
15.1-a6 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $8.942806850$ 0.288627850 \( -\frac{46942}{15} a + \frac{772631}{15} \) \( \bigl[a\) , \( -a\) , \( a\) , \( -2 a + 5\) , \( 2\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-a{x}^2+\left(-2a+5\right){x}+2$
15.1-a7 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $4.471403425$ 0.288627850 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-5{x}+2$
15.1-a8 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117850856$ 0.288627850 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-135{x}-660$
15.1-a9 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $2.235701712$ 0.288627850 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-80{x}+242$
15.1-a10 15.1-a \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558925428$ 0.288627850 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+{x}^2-2160{x}-39540$
15.1-b1 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $0.558925428$ 1.154511400 \( -\frac{147281603041}{215233605} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 109 a + 327\) , \( -2310 a + 5390\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(109a+327\right){x}-2310a+5390$
15.1-b2 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.942806850$ 1.154511400 \( -\frac{1}{15} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a - 3\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-a-3\right){x}$
15.1-b3 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117850856$ 1.154511400 \( \frac{4733169839}{3515625} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -36 a - 108\) , \( -189 a + 441\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(-36a-108\right){x}-189a+441$
15.1-b4 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.235701712$ 1.154511400 \( \frac{111284641}{50625} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 9 a + 27\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(9a+27\right){x}$
15.1-b5 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.942806850$ 1.154511400 \( \frac{46942}{15} a + \frac{725689}{15} \) \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -2\) , \( 1\bigr] \) ${y}^2+{x}{y}+a{y}={x}^3+\left(-a-1\right){x}^2-2{x}+1$
15.1-b6 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $8.942806850$ 1.154511400 \( -\frac{46942}{15} a + \frac{772631}{15} \) \( \bigl[1\) , \( a + 1\) , \( a\) , \( a - 2\) , \( -1\bigr] \) ${y}^2+{x}{y}+a{y}={x}^3+\left(a+1\right){x}^2+\left(a-2\right){x}-1$
15.1-b7 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.471403425$ 1.154511400 \( \frac{13997521}{225} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 4 a + 12\) , \( 21 a - 49\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(4a+12\right){x}+21a-49$
15.1-b8 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.117850856$ 1.154511400 \( \frac{272223782641}{164025} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 134 a + 402\) , \( -1575 a + 3675\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(134a+402\right){x}-1575a+3675$
15.1-b9 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.235701712$ 1.154511400 \( \frac{56667352321}{15} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 79 a + 237\) , \( 966 a - 2254\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(79a+237\right){x}+966a-2254$
15.1-b10 15.1-b \(\Q(\sqrt{-15}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.558925428$ 1.154511400 \( \frac{1114544804970241}{405} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2159 a + 6477\) , \( -112140 a + 261660\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a-1\right){x}^2+\left(2159a+6477\right){x}-112140a+261660$
36.2-a1 36.2-a \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( \frac{195836835}{512} a - \frac{122683695}{128} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 21 a + 141\) , \( 393 a - 550\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(21a+141\right){x}+393a-550$
36.2-a2 36.2-a \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( -\frac{195836835}{512} a - \frac{294897945}{512} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -5 a - 36\) , \( 17 a + 92\bigr] \) ${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(-5a-36\right){x}+17a+92$
36.2-a3 36.2-a \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $6.014860114$ 1.035353469 \( \frac{69255}{64} a - \frac{95715}{64} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(a+1\right){x}+a+2$
36.2-a4 36.2-a \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $6.014860114$ 1.035353469 \( -\frac{69255}{64} a - \frac{6615}{16} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -1\) , \( 1\bigr] \) ${y}^2+{x}{y}+a{y}={x}^3-{x}^2-{x}+1$
36.2-a5 36.2-a \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( \frac{103889505}{262144} a + \frac{64790715}{65536} \) \( \bigl[1\) , \( -1\) , \( a\) , \( -5 a + 9\) , \( -4 a - 5\bigr] \) ${y}^2+{x}{y}+a{y}={x}^3-{x}^2+\left(-5a+9\right){x}-4a-5$
36.2-a6 36.2-a \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( -\frac{103889505}{262144} a + \frac{363052365}{262144} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24 a + 6\) , \( -45 a + 24\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-24a+6\right){x}-45a+24$
36.2-b1 36.2-b \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( \frac{195836835}{512} a - \frac{122683695}{128} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 4 a - 41\) , \( -18 a + 109\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(4a-41\right){x}-18a+109$
36.2-b2 36.2-b \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( -\frac{195836835}{512} a - \frac{294897945}{512} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -23 a + 164\) , \( -394 a - 156\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-23a+164\right){x}-394a-156$
36.2-b3 36.2-b \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $6.014860114$ 1.035353469 \( \frac{69255}{64} a - \frac{95715}{64} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -a - 1\) , \( -a + 1\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(-a-1\right){x}-a+1$
36.2-b4 36.2-b \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $6.014860114$ 1.035353469 \( -\frac{69255}{64} a - \frac{6615}{16} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(-3a+4\right){x}-2a+4$
36.2-b5 36.2-b \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( \frac{103889505}{262144} a + \frac{64790715}{65536} \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 16\) , \( 44 a - 20\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+\left(-a+1\right){x}^2+\left(22a-16\right){x}+44a-20$
36.2-b6 36.2-b \(\Q(\sqrt{-15}) \) \( 2^{2} \cdot 3^{2} \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.004953371$ 1.035353469 \( -\frac{103889505}{262144} a + \frac{363052365}{262144} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 4 a + 4\) , \( 3 a - 9\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^3-{x}^2+\left(4a+4\right){x}+3a-9$
38.2-a1 38.2-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.647328640$ $6.697069272$ 0.559672526 \( \frac{12739275}{76} a - \frac{10237347}{76} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 2 a - 2\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(2a-2\right){x}-4$
38.2-a2 38.2-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.323664320$ $6.697069272$ 0.559672526 \( \frac{321975}{5776} a + \frac{7490853}{5776} \) \( \bigl[a\) , \( -1\) , \( a\) , \( a + 4\) , \( -2 a\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(a+4\right){x}-2a$
38.2-a3 38.2-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.161832160$ $6.697069272$ 0.559672526 \( -\frac{420795}{4864} a + \frac{11009439}{4864} \) \( \bigl[1\) , \( a\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+a{x}^2-{x}$
38.2-a4 38.2-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.161832160$ $3.348534636$ 0.559672526 \( -\frac{53581589505}{521284} a + \frac{17808923169}{521284} \) \( \bigl[a\) , \( -1\) , \( a\) , \( 16 a + 24\) , \( -26 a + 96\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3-{x}^2+\left(16a+24\right){x}-26a+96$
38.2-b1 38.2-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.697069272$ 1.729175850 \( \frac{12739275}{76} a - \frac{10237347}{76} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -5 a - 7\) , \( 5 a + 10\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(-5a-7\right){x}+5a+10$
38.2-b2 38.2-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.697069272$ 1.729175850 \( \frac{321975}{5776} a + \frac{7490853}{5776} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -a - 1\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-a-1\right){x}-1$
38.2-b3 38.2-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $6.697069272$ 1.729175850 \( -\frac{420795}{4864} a + \frac{11009439}{4864} \) \( \bigl[a\) , \( a\) , \( 0\) , \( 2 a - 3\) , \( -2\bigr] \) ${y}^2+a{x}{y}={x}^3+a{x}^2+\left(2a-3\right){x}-2$
38.2-b4 38.2-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.348534636$ 1.729175850 \( -\frac{53581589505}{521284} a + \frac{17808923169}{521284} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -6 a - 1\) , \( 6 a - 17\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2+\left(-6a-1\right){x}+6a-17$
38.3-a1 38.3-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.161832160$ $3.348534636$ 0.559672526 \( \frac{53581589505}{521284} a - \frac{8943166584}{130321} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -18 a + 40\) , \( 25 a + 70\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-18a+40\right){x}+25a+70$
38.3-a2 38.3-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.323664320$ $6.697069272$ 0.559672526 \( -\frac{321975}{5776} a + \frac{1953207}{1444} \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -3 a + 5\) , \( a - 2\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^3+\left(-a-1\right){x}^2+\left(-3a+5\right){x}+a-2$
38.3-a3 38.3-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.161832160$ $6.697069272$ 0.559672526 \( \frac{420795}{4864} a + \frac{2647161}{1216} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-{x}$
38.3-a4 38.3-a \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $0.647328640$ $6.697069272$ 0.559672526 \( -\frac{12739275}{76} a + \frac{625482}{19} \) \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -2 a\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+\left(-a+1\right){x}^2-2a{x}-4$
38.3-b1 38.3-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $3.348534636$ 1.729175850 \( \frac{53581589505}{521284} a - \frac{8943166584}{130321} \) \( \bigl[1\) , \( a\) , \( 1\) , \( 6 a - 7\) , \( -6 a - 11\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(6a-7\right){x}-6a-11$
38.3-b2 38.3-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.697069272$ 1.729175850 \( -\frac{321975}{5776} a + \frac{1953207}{1444} \) \( \bigl[1\) , \( a\) , \( 1\) , \( a - 2\) , \( -1\bigr] \) ${y}^2+{x}{y}+{y}={x}^3+a{x}^2+\left(a-2\right){x}-1$
38.3-b3 38.3-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $6.697069272$ 1.729175850 \( \frac{420795}{4864} a + \frac{2647161}{1216} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -a - 3\) , \( -2 a + 6\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(-a-3\right){x}-2a+6$
38.3-b4 38.3-b \(\Q(\sqrt{-15}) \) \( 2 \cdot 19 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.697069272$ 1.729175850 \( -\frac{12739275}{76} a + \frac{625482}{19} \) \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( 6 a - 14\) , \( -11 a - 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^3+\left(a+1\right){x}^2+\left(6a-14\right){x}-11a-5$
48.1-a1 48.1-a \(\Q(\sqrt{-15}) \) \( 2^{4} \cdot 3 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.801619803$ $3.021529073$ 0.702771756 \( \frac{38043647}{3} a - \frac{37451518}{3} \) \( \bigl[a\) , \( 1\) , \( a\) , \( 5 a - 105\) , \( -41 a + 423\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^3+{x}^2+\left(5a-105\right){x}-41a+423$
48.1-a2 48.1-a \(\Q(\sqrt{-15}) \) \( 2^{4} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.225202475$ $6.043058147$ 0.702771756 \( \frac{774151}{3} a - 404740 \) \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -a + 15\) , \( -6 a - 3\bigr] \) ${y}^2+a{x}{y}={x}^3+\left(a-1\right){x}^2+\left(-a+15\right){x}-6a-3$
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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.