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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
16.1-a1 16.1-a \(\Q(\sqrt{51}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.054516910$ $18.51924189$ 5.327799054 \( -27648 \) \( \bigl[0\) , \( a\) , \( a + 1\) , \( 16\) , \( a - 13\bigr] \) ${y}^2+\left(w+1\right){y}={x}^3+w{x}^2+16{x}+w-13$
16.1-b1 16.1-b \(\Q(\sqrt{51}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $2.054516910$ $18.51924189$ 5.327799054 \( -27648 \) \( \bigl[0\) , \( -a\) , \( a + 1\) , \( 16\) , \( -2 a - 13\bigr] \) ${y}^2+\left(w+1\right){y}={x}^3-w{x}^2+16{x}-2w-13$
16.1-c1 16.1-c \(\Q(\sqrt{51}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.595981725$ $18.51924189$ 1.545507295 \( -27648 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( -9\) , \( -2 a - 13\bigr] \) ${y}^2+\left(w+1\right){y}={x}^3-9{x}-2w-13$
16.1-d1 16.1-d \(\Q(\sqrt{51}) \) \( 2^{4} \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.595981725$ $18.51924189$ 1.545507295 \( -27648 \) \( \bigl[0\) , \( 0\) , \( a + 1\) , \( -9\) , \( a - 13\bigr] \) ${y}^2+\left(w+1\right){y}={x}^3-9{x}+w-13$
17.1-a1 17.1-a \(\Q(\sqrt{51}) \) \( 17 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.539083304$ 4.222731281 \( -\frac{35937}{83521} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 377\bigr] \) ${y}^2+{x}{y}={x}^3-{x}^2-6{x}+377$
17.1-a2 17.1-a \(\Q(\sqrt{51}) \) \( 17 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $30.15633321$ 4.222731281 \( \frac{35937}{17} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( -1\bigr] \) ${y}^2+{x}{y}={x}^3-{x}^2-6{x}-1$
17.1-a3 17.1-a \(\Q(\sqrt{51}) \) \( 17 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $30.15633321$ 4.222731281 \( \frac{20346417}{289} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -51\) , \( 152\bigr] \) ${y}^2+{x}{y}={x}^3-{x}^2-51{x}+152$
17.1-a4 17.1-a \(\Q(\sqrt{51}) \) \( 17 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $30.15633321$ 4.222731281 \( \frac{82483294977}{17} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -816\) , \( 9179\bigr] \) ${y}^2+{x}{y}={x}^3-{x}^2-816{x}+9179$
17.1-b1 17.1-b \(\Q(\sqrt{51}) \) \( 17 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $11.00049651$ $2.393455763$ 3.686825688 \( -\frac{35937}{83521} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 48\) , \( -325\bigr] \) ${y}^2+w{x}{y}={x}^3+48{x}-325$
17.1-b2 17.1-b \(\Q(\sqrt{51}) \) \( 17 \) $2$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.750124128$ $38.29529222$ 3.686825688 \( \frac{35937}{17} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 48\) , \( 53\bigr] \) ${y}^2+w{x}{y}={x}^3+48{x}+53$
17.1-b3 17.1-b \(\Q(\sqrt{51}) \) \( 17 \) $2$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $11.00049651$ $9.573823055$ 3.686825688 \( \frac{20346417}{289} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( -280\bigr] \) ${y}^2+w{x}{y}={x}^3+3{x}-280$
17.1-b4 17.1-b \(\Q(\sqrt{51}) \) \( 17 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $11.00049651$ $2.393455763$ 3.686825688 \( \frac{82483294977}{17} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -762\) , \( -12367\bigr] \) ${y}^2+w{x}{y}={x}^3-762{x}-12367$
17.1-c1 17.1-c \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.036297434$ $7.539083304$ 1.074842109 \( -\frac{35937}{83521} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 28\) , \( 75\bigr] \) ${y}^2+w{x}{y}+w{y}={x}^3+28{x}+75$
17.1-c2 17.1-c \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.509074358$ $30.15633321$ 1.074842109 \( \frac{35937}{17} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 28\) , \( 61\bigr] \) ${y}^2+w{x}{y}+w{y}={x}^3+28{x}+61$
17.1-c3 17.1-c \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.018148717$ $30.15633321$ 1.074842109 \( \frac{20346417}{289} \) \( \bigl[a\) , \( 0\) , \( a\) , \( 23\) , \( 45\bigr] \) ${y}^2+w{x}{y}+w{y}={x}^3+23{x}+45$
17.1-c4 17.1-c \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $2.036297434$ $30.15633321$ 1.074842109 \( \frac{82483294977}{17} \) \( \bigl[a\) , \( 0\) , \( a\) , \( -62\) , \( 11\bigr] \) ${y}^2+w{x}{y}+w{y}={x}^3-62{x}+11$
17.1-d1 17.1-d \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $13.65757227$ $2.393455763$ 2.288673435 \( -\frac{35937}{83521} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}-14$
17.1-d2 17.1-d \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $3.414393067$ $38.29529222$ 2.288673435 \( \frac{35937}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-{x}$
17.1-d3 17.1-d \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $6.828786135$ $9.573823055$ 2.288673435 \( \frac{20346417}{289} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-6{x}-4$
17.1-d4 17.1-d \(\Q(\sqrt{51}) \) \( 17 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $13.65757227$ $2.393455763$ 2.288673435 \( \frac{82483294977}{17} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \) ${y}^2+{x}{y}+{y}={x}^3-{x}^2-91{x}-310$
24.1-a1 24.1-a \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.540027220$ $2.325279868$ 6.616350463 \( \frac{207646}{6561} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 24687 a + 176301\) , \( -41091534 a - 293452249\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(24687w+176301\right){x}-41091534w-293452249$
24.1-a2 24.1-a \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.270013610$ $18.60223895$ 6.616350463 \( \frac{2048}{3} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \) ${y}^2={x}^3+6{x}+7$
24.1-a3 24.1-a \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.540027220$ $37.20447790$ 6.616350463 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -6813 a - 48654\) , \( 560799 a + 4004906\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(-6813w-48654\right){x}+560799w+4004906$
24.1-a4 24.1-a \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $5.080054440$ $9.301119475$ 6.616350463 \( \frac{1556068}{81} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 38336 a - 273635\) , \( 10427941 a - 74469977\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(38336w-273635\right){x}+10427941w-74469977$
24.1-a5 24.1-a \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $5.080054440$ $37.20447790$ 6.616350463 \( \frac{28756228}{3} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -101313 a - 723519\) , \( 46145736 a + 329546471\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(-101313w-723519\right){x}+46145736w+329546471$
24.1-a6 24.1-a \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $10.16010888$ $2.325279868$ 6.616350463 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 605336 a - 4322825\) , \( 685333873 a - 4894262387\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(605336w-4322825\right){x}+685333873w-4894262387$
24.1-b1 24.1-b \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $5.683508517$ 0.795850378 \( \frac{207646}{6561} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2746 a + 19640\) , \( -1543982 a + 11026268\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3-w{x}^2+\left(-2746w+19640\right){x}-1543982w+11026268$
24.1-b2 24.1-b \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $11.36701703$ 0.795850378 \( \frac{2048}{3} \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^3+{x}^2+{x}$
24.1-b3 24.1-b \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $22.73403407$ 0.795850378 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -754 a - 5355\) , \( -26862 a - 191802\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(-754w-5355\right){x}-26862w-191802$
24.1-b4 24.1-b \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $22.73403407$ 0.795850378 \( \frac{1556068}{81} \) \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 4254 a - 30350\) , \( -362098 a + 2585928\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3-w{x}^2+\left(4254w-30350\right){x}-362098w+2585928$
24.1-b5 24.1-b \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $5.683508517$ 0.795850378 \( \frac{28756228}{3} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -11254 a - 80340\) , \( -1799688 a - 12852312\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(-11254w-80340\right){x}-1799688w-12852312$
24.1-b6 24.1-b \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $22.73403407$ 0.795850378 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -67254 a - 480260\) , \( 25001614 a + 178547268\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(-67254w-480260\right){x}+25001614w+178547268$
24.1-c1 24.1-c \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.492303742$ $5.683508517$ 4.750601994 \( \frac{207646}{6561} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 24686 a + 176275\) , \( 41465209 a + 296120813\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(24686w+176275\right){x}+41465209w+296120813$
24.1-c2 24.1-c \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $11.93842994$ $11.36701703$ 4.750601994 \( \frac{2048}{3} \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \) ${y}^2={x}^3+6{x}-7$
24.1-c3 24.1-c \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $5.969214971$ $22.73403407$ 4.750601994 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -6814 a - 48680\) , \( -664079 a - 4742482\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(-6814w-48680\right){x}-664079w-4742482$
24.1-c4 24.1-c \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.984607485$ $22.73403407$ 4.750601994 \( \frac{1556068}{81} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 38337 a - 273609\) , \( -10394976 a + 74235411\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(38337w-273609\right){x}-10394976w+74235411$
24.1-c5 24.1-c \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.984607485$ $5.683508517$ 4.750601994 \( \frac{28756228}{3} \) \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -101314 a - 723545\) , \( -47679881 a - 340502467\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(w-1\right){x}^2+\left(-101314w-723545\right){x}-47679881w-340502467$
24.1-c6 24.1-c \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.492303742$ $22.73403407$ 4.750601994 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 605337 a - 4322799\) , \( -684814098 a + 4890551301\bigr] \) ${y}^2+\left(w+1\right){x}{y}={x}^3+\left(w-1\right){x}^2+\left(605337w-4322799\right){x}-684814098w+4890551301$
24.1-d1 24.1-d \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.325279868$ 0.651208618 \( \frac{207646}{6561} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2738 a + 19623\) , \( 1519308 a - 10849845\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+{x}^2+\left(-2738w+19623\right){x}+1519308w-10849845$
24.1-d2 24.1-d \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $18.60223895$ 0.651208618 \( \frac{2048}{3} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \) ${y}^2={x}^3-{x}^2+{x}$
24.1-d3 24.1-d \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $37.20447790$ 0.651208618 \( \frac{35152}{9} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -764 a - 5372\) , \( 20035 a + 143270\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(-w+1\right){x}^2+\left(-764w-5372\right){x}+20035w+143270$
24.1-d4 24.1-d \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.301119475$ 0.651208618 \( \frac{1556068}{81} \) \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 4262 a - 30367\) , \( 400424 a - 2859415\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+{x}^2+\left(4262w-30367\right){x}+400424w-2859415$
24.1-d5 24.1-d \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $37.20447790$ 0.651208618 \( \frac{28756228}{3} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -11264 a - 80357\) , \( 1698361 a + 12128915\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(-w+1\right){x}^2+\left(-11264w-80357\right){x}+1698361w+12128915$
24.1-d6 24.1-d \(\Q(\sqrt{51}) \) \( 2^{3} \cdot 3 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $2.325279868$ 0.651208618 \( \frac{3065617154}{9} \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -67264 a - 480277\) , \( -25606941 a - 182869945\bigr] \) ${y}^2+\left(w+1\right){x}{y}+\left(w+1\right){y}={x}^3+\left(-w+1\right){x}^2+\left(-67264w-480277\right){x}-25606941w-182869945$
25.2-a1 25.2-a \(\Q(\sqrt{51}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 0.514337188 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 24 a + 155\bigr] \) ${y}^2+{y}={x}^3+24w+155$
25.2-a2 25.2-a \(\Q(\sqrt{51}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 0.514337188 \( 0 \) \( \bigl[0\) , \( a\) , \( 1\) , \( 17\) , \( a - 6\bigr] \) ${y}^2+{y}={x}^3+w{x}^2+17{x}+w-6$
25.2-b1 25.2-b \(\Q(\sqrt{51}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 4.629034696 \( 0 \) \( \bigl[0\) , \( -a\) , \( a\) , \( 17\) , \( -a - 7\bigr] \) ${y}^2+w{y}={x}^3-w{x}^2+17{x}-w-7$
25.2-b2 25.2-b \(\Q(\sqrt{51}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 4.629034696 \( 0 \) \( \bigl[0\) , \( 0\) , \( a\) , \( 0\) , \( -24 a - 168\bigr] \) ${y}^2+w{y}={x}^3-24w-168$
25.3-a1 25.3-a \(\Q(\sqrt{51}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 0.514337188 \( 0 \) \( \bigl[0\) , \( -a\) , \( 1\) , \( 17\) , \( -a - 6\bigr] \) ${y}^2+{y}={x}^3-w{x}^2+17{x}-w-6$
25.3-a2 25.3-a \(\Q(\sqrt{51}) \) \( 5^{2} \) 0 $\mathsf{trivial}$ $-3$ $N(\mathrm{U}(1))$ $1$ $7.346204439$ 0.514337188 \( 0 \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -24 a + 155\bigr] \) ${y}^2+{y}={x}^3-24w+155$
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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.