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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
256.1-a1 256.1-a \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $14.78882033$ 1.793407891 \( -774198 a + 1983150 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( a + 1\) , \( -27 a - 42\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}-27a-42$
256.1-a2 256.1-a \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $3.697205083$ 1.793407891 \( -349618194 a + 895566564 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 16 a + 13\) , \( 32 a + 34\bigr] \) ${y}^2={x}^{3}+\left(16a+13\right){x}+32a+34$
256.1-a3 256.1-a \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $14.78882033$ 1.793407891 \( -8748 a + 25056 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -4 a - 7\) , \( 4 a + 6\bigr] \) ${y}^2={x}^{3}+\left(-4a-7\right){x}+4a+6$
256.1-a4 256.1-a \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $14.78882033$ 1.793407891 \( 8748 a + 16308 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( 4 a - 11\) , \( -4 a + 10\bigr] \) ${y}^2={x}^{3}+\left(4a-11\right){x}-4a+10$
256.1-a5 256.1-a \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $14.78882033$ 1.793407891 \( 774198 a + 1208952 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -a + 2\) , \( 27 a - 69\bigr] \) ${y}^2={x}^{3}+\left(-a+2\right){x}+27a-69$
256.1-a6 256.1-a \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $3.697205083$ 1.793407891 \( 349618194 a + 545948370 \) \( \bigl[0\) , \( 0\) , \( 0\) , \( -16 a + 29\) , \( -32 a + 66\bigr] \) ${y}^2={x}^{3}+\left(-16a+29\right){x}-32a+66$
256.1-b1 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -144 a + 360\) , \( -6784 a + 17392\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-144a+360\right){x}-6784a+17392$
256.1-b2 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( -\frac{110887}{256} a + \frac{66933}{64} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -16 a - 24\) , \( -256 a - 400\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-16a-24\right){x}-256a-400$
256.1-b3 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 144 a + 216\) , \( 6784 a + 10608\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(144a+216\right){x}+6784a+10608$
256.1-b4 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( \frac{110887}{256} a + \frac{156845}{256} \) \( \bigl[0\) , \( -1\) , \( 0\) , \( 16 a - 40\) , \( 256 a - 656\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(16a-40\right){x}+256a-656$
256.1-b5 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $5.918369177$ 1.435415367 \( -\frac{915957}{16} a + \frac{2374013}{16} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 28\) , \( -16 a - 28\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15a-28\right){x}-16a-28$
256.1-b6 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 15697 a - 40284\) , \( -1536816 a + 3936512\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(15697a-40284\right){x}-1536816a+3936512$
256.1-b7 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $5.918369177$ 1.435415367 \( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 977 a - 2524\) , \( -23856 a + 61184\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(977a-2524\right){x}-23856a+61184$
256.1-b8 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $5.918369177$ 1.435415367 \( \frac{915957}{16} a + \frac{182257}{2} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 17 a - 44\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(17a-44\right){x}$
256.1-b9 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -175 a - 348\) , \( 1936 a + 2788\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-175a-348\right){x}+1936a+2788$
256.1-b10 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $5.918369177$ 1.435415367 \( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -975 a - 1548\) , \( 22880 a + 35780\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-975a-1548\right){x}+22880a+35780$
256.1-b11 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( \frac{54503407609}{4} a + \frac{42555672073}{2} \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 177 a - 524\) , \( -2112 a + 5248\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(177a-524\right){x}-2112a+5248$
256.1-b12 256.1-b \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $2.959184588$ 1.435415367 \( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15695 a - 24588\) , \( 1521120 a + 2375108\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(-15695a-24588\right){x}+1521120a+2375108$
256.1-c1 256.1-c \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/4\Z$ $1$ $11.99882659$ 1.455071453 \( -292271882500 a + 748669862250 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -267 a - 420\) , \( 7254 a + 11336\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-267a-420\right){x}+7254a+11336$
256.1-c2 256.1-c \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $11.99882659$ 1.455071453 \( -20500 a + 54000 \) \( \bigl[0\) , \( a\) , \( 0\) , \( 2 a - 2\) , \( a - 1\bigr] \) ${y}^2={x}^{3}+a{x}^{2}+\left(2a-2\right){x}+a-1$
256.1-c3 256.1-c \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $23.99765318$ 1.455071453 \( 2000 \) \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -27 a - 40\) , \( 26 a + 40\bigr] \) ${y}^2={x}^{3}+\left(a-1\right){x}^{2}+\left(-27a-40\right){x}+26a+40$
256.1-c4 256.1-c \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $11.99882659$ 1.455071453 \( 20500 a + 33500 \) \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a\) , \( -a\bigr] \) ${y}^2={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$
256.1-c5 256.1-c \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z\oplus\Z/4\Z$ $1$ $23.99765318$ 1.455071453 \( 1098500 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 347 a - 887\) , \( -4862 a + 12454\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(347a-887\right){x}-4862a+12454$
256.1-c6 256.1-c \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/4\Z$ $1$ $11.99882659$ 1.455071453 \( 292271882500 a + 456397979750 \) \( \bigl[0\) , \( -a\) , \( 0\) , \( 267 a - 687\) , \( -7254 a + 18590\bigr] \) ${y}^2={x}^{3}-a{x}^{2}+\left(267a-687\right){x}-7254a+18590$
256.1-d1 256.1-d \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $26.12924634$ 1.584318273 \( -50671167248 a + 129796414656 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -38 a - 77\) , \( 268 a + 444\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-38a-77\right){x}+268a+444$
256.1-d2 256.1-d \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $26.12924634$ 1.584318273 \( -1552 a + 4288 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(2a+3\right){x}$
256.1-d3 256.1-d \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $26.12924634$ 1.584318273 \( 1552 a + 2736 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4\) , \( -a + 4\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+4{x}-a+4$
256.1-d4 256.1-d \(\Q(\sqrt{17}) \) \( 2^{8} \) $0$ $\Z/2\Z$ $1$ $26.12924634$ 1.584318273 \( 50671167248 a + 79125247408 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 40 a - 116\) , \( -229 a + 596\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(40a-116\right){x}-229a+596$
256.1-e1 256.1-e \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $0.134949823$ $8.500633610$ 2.225815404 \( -343 a + 1029 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 4\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(a+4\right){x}$
256.1-e2 256.1-e \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/4\Z$ $1.079598584$ $8.500633610$ 2.225815404 \( -2701312025 a + 6919553753 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 16 a - 8\) , \( -48 a - 12\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(16a-8\right){x}-48a-12$
256.1-e3 256.1-e \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.539799292$ $17.00126722$ 2.225815404 \( -24225 a + 68453 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a - 8\) , \( -8 a - 12\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-4a-8\right){x}-8a-12$
256.1-e4 256.1-e \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.269899646$ $17.00126722$ 2.225815404 \( 1995 a + 5021 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 25 a - 60\) , \( 24 a - 60\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(25a-60\right){x}+24a-60$
256.1-e5 256.1-e \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $1.079598584$ $8.500633610$ 2.225815404 \( 7659605 a + 11960871 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( a - 4\) , \( -22 a + 56\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(a-4\right){x}-22a+56$
256.1-e6 256.1-e \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $0.539799292$ $8.500633610$ 2.225815404 \( 21069823 a + 33751811 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 305 a - 780\) , \( 4096 a - 10492\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(305a-780\right){x}+4096a-10492$
256.1-f1 256.1-f \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $1.079598584$ $8.500633610$ 2.225815404 \( -7659605 a + 19620476 \) \( \bigl[0\) , \( -1\) , \( 0\) , \( -a - 3\) , \( 22 a + 34\bigr] \) ${y}^2={x}^{3}-{x}^{2}+\left(-a-3\right){x}+22a+34$
256.1-f2 256.1-f \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $0.134949823$ $8.500633610$ 2.225815404 \( 343 a + 686 \) \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 4\) , \( 4\bigr] \) ${y}^2={x}^{3}+\left(a+1\right){x}^{2}+\left(a+4\right){x}+4$
256.1-f3 256.1-f \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.269899646$ $17.00126722$ 2.225815404 \( -1995 a + 7016 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -23 a - 36\) , \( 0\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-23a-36\right){x}$
256.1-f4 256.1-f \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.539799292$ $17.00126722$ 2.225815404 \( 24225 a + 44228 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( 4 a - 12\) , \( 8 a - 20\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(4a-12\right){x}+8a-20$
256.1-f5 256.1-f \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/2\Z$ $0.539799292$ $8.500633610$ 2.225815404 \( -21069823 a + 54821634 \) \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -303 a - 476\) , \( -3792 a - 5920\bigr] \) ${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+\left(-303a-476\right){x}-3792a-5920$
256.1-f6 256.1-f \(\Q(\sqrt{17}) \) \( 2^{8} \) $1$ $\Z/4\Z$ $1.079598584$ $8.500633610$ 2.225815404 \( 2701312025 a + 4218241728 \) \( \bigl[0\) , \( 1\) , \( 0\) , \( -16 a + 8\) , \( 48 a - 60\bigr] \) ${y}^2={x}^{3}+{x}^{2}+\left(-16a+8\right){x}+48a-60$
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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.