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Results (28 matches)

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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
77.1-a1 77.1-a \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $6.801526433$ $42.50483853$ 3.660638887 \( -\frac{3620807}{77} a - \frac{13473085}{77} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 7 a + 15\) , \( 4 a + 52\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(7a+15\right){x}+4a+52$
77.1-a2 77.1-a \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.267175477$ $4.722759837$ 3.660638887 \( -\frac{4739950783}{65219} a + \frac{23189184708}{65219} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 42 a - 155\) , \( 228 a - 1038\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(42a-155\right){x}+228a-1038$
77.1-a3 77.1-a \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.534350955$ $2.361379918$ 3.660638887 \( -\frac{1921257763497199}{41503} a + \frac{9390113368382893}{41503} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 592 a - 2850\) , \( 15694 a - 76652\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(592a-2850\right){x}+15694a-76652$
77.1-a4 77.1-a \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $13.60305286$ $21.25241926$ 3.660638887 \( \frac{1443189816791}{77} a + \frac{5610375344526}{77} \) \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 12 a - 15\) , \( 20 a - 44\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(12a-15\right){x}+20a-44$
77.1-b1 77.1-b \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $2$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.192052107$ $10.23860076$ 3.585372697 \( \frac{884736}{539} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 2\) , \( 0\bigr] \) ${y}^2+{y}={x}^{3}+2{x}$
77.1-c1 77.1-c \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( \frac{3620807}{77} a - \frac{17093892}{77} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 5 a - 8\) , \( 10 a - 33\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(5a-8\right){x}+10a-33$
77.1-c2 77.1-c \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( -\frac{1443189816791}{77} a + \frac{7053565161317}{77} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 55 a - 253\) , \( 466 a - 2263\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(55a-253\right){x}+466a-2263$
77.1-c3 77.1-c \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( \frac{4739950783}{65219} a + \frac{18449233925}{65219} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -5 a + 37\) , \( 34 a - 157\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-5a+37\right){x}+34a-157$
77.1-c4 77.1-c \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( \frac{1921257763497199}{41503} a + \frac{7468855604885694}{41503} \) \( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 50 a - 293\) , \( 430 a - 2049\bigr] \) ${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(50a-293\right){x}+430a-2049$
77.1-d1 77.1-d \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.438142950$ $3.210187340$ 3.846910527 \( \frac{4657463}{41503} \) \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 36 a + 137\) , \( -619 a - 2411\bigr] \) ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(36a+137\right){x}-619a-2411$
77.1-d2 77.1-d \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $2$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.438142950$ $3.210187340$ 3.846910527 \( \frac{15124197817}{1294139} \) \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 469 a - 2246\) , \( 10656 a - 52022\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(469a-2246\right){x}+10656a-52022$
77.1-e1 77.1-e \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $0.380901696$ $21.59210152$ 1.666249113 \( -\frac{78843215872}{539} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -89\) , \( 295\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-89{x}+295$
77.1-e2 77.1-e \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/3\Z$ $\mathrm{SU}(2)$ $1.142705089$ $2.399122391$ 1.666249113 \( -\frac{13278380032}{156590819} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( -49\) , \( 600\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}-49{x}+600$
77.1-e3 77.1-e \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $3.428115269$ $0.266569154$ 1.666249113 \( \frac{9463555063808}{115539436859} \) \( \bigl[0\) , \( 1\) , \( 1\) , \( 441\) , \( -15815\bigr] \) ${y}^2+{y}={x}^{3}+{x}^{2}+441{x}-15815$
77.1-f1 77.1-f \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $6.801526433$ $42.50483853$ 3.660638887 \( \frac{3620807}{77} a - \frac{17093892}{77} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( 3 a + 4\) , \( 2 a + 4\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(3a+4\right){x}+2a+4$
77.1-f2 77.1-f \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/6\Z$ $\mathrm{SU}(2)$ $13.60305286$ $21.25241926$ 3.660638887 \( -\frac{1443189816791}{77} a + \frac{7053565161317}{77} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -2 a - 21\) , \( -44 a - 171\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-2a-21\right){x}-44a-171$
77.1-f3 77.1-f \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $2.267175477$ $4.722759837$ 3.660638887 \( \frac{4739950783}{65219} a + \frac{18449233925}{65219} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -32 a - 131\) , \( -392 a - 1527\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-32a-131\right){x}-392a-1527$
77.1-f4 77.1-f \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.534350955$ $2.361379918$ 3.660638887 \( \frac{1921257763497199}{41503} a + \frac{7468855604885694}{41503} \) \( \bigl[a\) , \( a + 1\) , \( a\) , \( -582 a - 2276\) , \( -18553 a - 72125\bigr] \) ${y}^2+a{x}{y}+a{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-582a-2276\right){x}-18553a-72125$
77.1-g1 77.1-g \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( -\frac{3620807}{77} a - \frac{13473085}{77} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -6 a - 2\) , \( -10 a - 23\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-6a-2\right){x}-10a-23$
77.1-g2 77.1-g \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( -\frac{4739950783}{65219} a + \frac{23189184708}{65219} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( 4 a + 33\) , \( -34 a - 123\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4a+33\right){x}-34a-123$
77.1-g3 77.1-g \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( -\frac{1921257763497199}{41503} a + \frac{9390113368382893}{41503} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -51 a - 242\) , \( -430 a - 1619\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-51a-242\right){x}-430a-1619$
77.1-g4 77.1-g \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $7.332154545$ 1.671153117 \( \frac{1443189816791}{77} a + \frac{5610375344526}{77} \) \( \bigl[a\) , \( -a\) , \( 1\) , \( -56 a - 197\) , \( -466 a - 1797\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(-56a-197\right){x}-466a-1797$
77.1-h1 77.1-h \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\mathsf{trivial}$ $\mathrm{SU}(2)$ $0.175784754$ $9.086092621$ 2.912279051 \( \frac{884736}{539} \) \( \bigl[0\) , \( 0\) , \( 1\) , \( 18 a + 70\) , \( -20 a - 78\bigr] \) ${y}^2+{y}={x}^{3}+\left(18a+70\right){x}-20a-78$
77.1-i1 77.1-i \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.847304922$ $7.031061357$ 2.715659066 \( \frac{4657463}{41503} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( 4\) , \( 11\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}+4{x}+11$
77.1-i2 77.1-i \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.694609845$ $7.031061357$ 2.715659066 \( \frac{15124197817}{1294139} \) \( \bigl[1\) , \( 1\) , \( 0\) , \( -51\) , \( 110\bigr] \) ${y}^2+{x}{y}={x}^{3}+{x}^{2}-51{x}+110$
77.1-j1 77.1-j \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.602881548$ 1.099275660 \( -\frac{78843215872}{539} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -803 a - 3120\) , \( -24422 a - 94941\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-803a-3120\right){x}-24422a-94941$
77.1-j2 77.1-j \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.602881548$ 1.099275660 \( -\frac{13278380032}{156590819} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -443 a - 1720\) , \( -48462 a - 188396\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-443a-1720\right){x}-48462a-188396$
77.1-j3 77.1-j \(\Q(\sqrt{77}) \) \( 7 \cdot 11 \) 0 $\mathsf{trivial}$ $\mathrm{SU}(2)$ $1$ $0.602881548$ 1.099275660 \( \frac{9463555063808}{115539436859} \) \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 3967 a + 15430\) , \( 1269148 a + 4933819\bigr] \) ${y}^2+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(3967a+15430\right){x}+1269148a+4933819$
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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.