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Label Class Base field Conductor norm Rank Torsion CM Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
128.6-a1 128.6-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/4\Z$ $1$ $8.823675287$ 2.140055600 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[a\) , \( a\) , \( a\) , \( a\) , \( a\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+a{x}^{2}+a{x}+a$
128.6-a2 128.6-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.411837643$ 2.140055600 \( -\frac{23841914775}{2} a + 30536164178 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -99 a - 157\) , \( -460 a - 721\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-99a-157\right){x}-460a-721$
128.6-a3 128.6-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $17.64735057$ 2.140055600 \( -\frac{159495}{4} a + 160181 \) \( \bigl[a\) , \( 1\) , \( a\) , \( -49 a - 77\) , \( 220 a + 343\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-49a-77\right){x}+220a+343$
128.6-a4 128.6-a \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $35.29470114$ 2.140055600 \( \frac{1592342311}{2} a + 1243265046 \) \( \bigl[a\) , \( -1\) , \( a\) , \( -a - 8\) , \( a + 2\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-{x}^{2}+\left(-a-8\right){x}+a+2$
128.6-b1 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -274 a + 703\) , \( -18518 a + 47435\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-274a+703\right){x}-18518a+47435$
128.6-b2 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( -\frac{110887}{256} a + \frac{66933}{64} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( -2 a - 1\) , \( -14 a - 21\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-2a-1\right){x}-14a-21$
128.6-b3 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) \( \bigl[a\) , \( 1\) , \( 0\) , \( 23 a + 19\) , \( 329 a + 535\bigr] \) ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(23a+19\right){x}+329a+535$
128.6-b4 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( \frac{110887}{256} a + \frac{156845}{256} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 89 a + 139\) , \( 57 a + 89\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(89a+139\right){x}+57a+89$
128.6-b5 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.369837957$ 1.014991940 \( -\frac{915957}{16} a + \frac{2374013}{16} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -9\) , \( -a - 7\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}-9{x}-a-7$
128.6-b6 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) \( \bigl[a\) , \( a\) , \( 0\) , \( -10853 a - 16976\) , \( -715483 a - 1117196\bigr] \) ${y}^2+a{x}{y}={x}^{3}+a{x}^{2}+\left(-10853a-16976\right){x}-715483a-1117196$
128.6-b7 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.369837957$ 1.014991940 \( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 1898 a - 4865\) , \( -64912 a + 166277\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(1898a-4865\right){x}-64912a+166277$
128.6-b8 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.369837957$ 1.014991940 \( \frac{915957}{16} a + \frac{182257}{2} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 33 a - 85\) , \( -13 a + 33\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(33a-85\right){x}-13a+33$
128.6-b9 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( 10 a - 129\) , \( 211 a - 247\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(10a-129\right){x}+211a-247$
128.6-b10 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.369837957$ 1.014991940 \( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -115 a - 229\) , \( 945 a + 1633\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-115a-229\right){x}+945a+1633$
128.6-b11 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( \frac{54503407609}{4} a + \frac{42555672073}{2} \) \( \bigl[a\) , \( -1\) , \( 0\) , \( 373 a - 965\) , \( -5721 a + 14641\bigr] \) ${y}^2+a{x}{y}={x}^{3}-{x}^{2}+\left(373a-965\right){x}-5721a+14641$
128.6-b12 128.6-b \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $4.184918978$ 1.014991940 \( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) \( \bigl[a\) , \( a - 1\) , \( a\) , \( -1995 a - 3269\) , \( 69553 a + 108129\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-1995a-3269\right){x}+69553a+108129$
128.6-c1 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $2.747663580$ 1.999218911 \( -\frac{55573026649}{16777216} a - \frac{85738862931}{16777216} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -24 a - 17\) , \( 98 a + 31\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-24a-17\right){x}+98a+31$
128.6-c2 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/4\Z$ $1$ $4.121495371$ 1.999218911 \( -\frac{110887}{256} a + \frac{66933}{64} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -20 a + 52\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-20a+52\right){x}$
128.6-c3 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/4\Z$ $1$ $1.373831790$ 1.999218911 \( \frac{55573026649}{16777216} a - \frac{35327972395}{4194304} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( 285 a - 728\) , \( 4041 a - 10348\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(285a-728\right){x}+4041a-10348$
128.6-c4 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $8.242990742$ 1.999218911 \( \frac{110887}{256} a + \frac{156845}{256} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( a + 3\) , \( -a + 3\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a+3\right){x}-a+3$
128.6-c5 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $16.48598148$ 1.999218911 \( -\frac{915957}{16} a + \frac{2374013}{16} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -146 a - 228\) , \( 0\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-146a-228\right){x}$
128.6-c6 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $0.686915895$ 1.999218911 \( -\frac{653762688677050897}{64} a + \frac{418661913522614865}{16} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 298 a - 1433\) , \( 6138 a - 22281\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(298a-1433\right){x}+6138a-22281$
128.6-c7 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $2.747663580$ 1.999218911 \( -\frac{203862548967}{4096} a + \frac{130566616997}{1024} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -22 a - 153\) , \( 314 a - 9\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-22a-153\right){x}+314a-9$
128.6-c8 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $8.242990742$ 1.999218911 \( \frac{915957}{16} a + \frac{182257}{2} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -7 a - 13\) , \( -39 a - 61\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-7a-13\right){x}-39a-61$
128.6-c9 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $16.48598148$ 1.999218911 \( -\frac{54503407609}{4} a + \frac{139614751755}{4} \) \( \bigl[a\) , \( 0\) , \( 0\) , \( -1656 a - 2588\) , \( 51666 a + 80680\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-1656a-2588\right){x}+51666a+80680$
128.6-c10 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z\oplus\Z/2\Z$ $1$ $5.495327161$ 1.999218911 \( \frac{203862548967}{4096} a + \frac{318403919021}{4096} \) \( \bigl[a\) , \( -a\) , \( a\) , \( 789 a - 2032\) , \( 16959 a - 43432\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(789a-2032\right){x}+16959a-43432$
128.6-c11 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $2.060747685$ 1.999218911 \( \frac{54503407609}{4} a + \frac{42555672073}{2} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -147 a - 253\) , \( -1763 a - 2797\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-147a-253\right){x}-1763a-2797$
128.6-c12 128.6-c \(\Q(\sqrt{17}) \) \( 2^{7} \) $0$ $\Z/2\Z$ $1$ $5.495327161$ 1.999218911 \( \frac{653762688677050897}{64} a + \frac{1020884965413408563}{64} \) \( \bigl[a\) , \( -a\) , \( a\) , \( 2429 a - 6352\) , \( -73585 a + 189080\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(2429a-6352\right){x}-73585a+189080$
128.6-d1 128.6-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $0.081969010$ $17.28603663$ 1.374613658 \( \frac{217}{16} a - \frac{139}{4} \) \( \bigl[a\) , \( -a\) , \( 0\) , \( -a\) , \( 197 a + 308\bigr] \) ${y}^2+a{x}{y}={x}^{3}-a{x}^{2}-a{x}+197a+308$
128.6-d2 128.6-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $0.327876043$ $17.28603663$ 1.374613658 \( -\frac{23841914775}{2} a + 30536164178 \) \( \bigl[a\) , \( 0\) , \( a\) , \( 31 a - 88\) , \( -142 a + 356\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(31a-88\right){x}-142a+356$
128.6-d3 128.6-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $0.163938021$ $34.57207326$ 1.374613658 \( -\frac{159495}{4} a + 160181 \) \( \bigl[a\) , \( 0\) , \( a\) , \( a - 8\) , \( -2 a + 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a-8\right){x}-2a+4$
128.6-d4 128.6-d \(\Q(\sqrt{17}) \) \( 2^{7} \) $1$ $\Z/2\Z$ $0.327876043$ $34.57207326$ 1.374613658 \( \frac{1592342311}{2} a + 1243265046 \) \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 83 a - 216\) , \( 136 a - 350\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(83a-216\right){x}+136a-350$
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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.