Learn more

Refine search


Results (12 matches)

  displayed columns for results
Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
15.2-a1 15.2-a 3.3.785.1 \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.839847852$ $18.99910249$ 1.708520240 \( \frac{805058590861631339}{576650390625} a^{2} + \frac{1268977584604502531}{576650390625} a - \frac{1562043547410087929}{576650390625} \) \( \bigl[a^{2} - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 75 a^{2} - 12 a - 472\) , \( 161 a^{2} - 42 a - 967\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(75a^{2}-12a-472\right){x}+161a^{2}-42a-967$
15.2-a2 15.2-a 3.3.785.1 \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.679695705$ $37.99820499$ 1.708520240 \( -\frac{25089380164}{759375} a^{2} - \frac{129708562831}{759375} a + \frac{498426941254}{759375} \) \( \bigl[a^{2} - 3\) , \( 1\) , \( a^{2} + a - 3\) , \( 55 a^{2} - 7 a - 352\) , \( 438 a^{2} - 88 a - 2686\bigr] \) ${y}^2+\left(a^{2}-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}+{x}^{2}+\left(55a^{2}-7a-352\right){x}+438a^{2}-88a-2686$
15.2-a3 15.2-a 3.3.785.1 \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.167969570$ $94.99551247$ 1.708520240 \( -\frac{474614682832216}{225} a^{2} + \frac{88887613981061}{225} a + \frac{2919928520246476}{225} \) \( \bigl[a^{2} + a - 3\) , \( -1\) , \( a^{2} + a - 3\) , \( 20 a^{2} + 3 a - 135\) , \( -95 a^{2} + 40 a + 541\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-{x}^{2}+\left(20a^{2}+3a-135\right){x}-95a^{2}+40a+541$
15.2-a4 15.2-a 3.3.785.1 \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.335939141$ $189.9910249$ 1.708520240 \( -\frac{7431769}{15} a^{2} - \frac{4179976}{15} a + \frac{60073024}{15} \) \( \bigl[a^{2} + a - 3\) , \( -1\) , \( a^{2} + a - 3\) , \( 8 a - 15\) , \( -4 a^{2} + 17 a - 3\bigr] \) ${y}^2+\left(a^{2}+a-3\right){x}{y}+\left(a^{2}+a-3\right){y}={x}^{3}-{x}^{2}+\left(8a-15\right){x}-4a^{2}+17a-3$
15.2-b1 15.2-b 3.3.785.1 \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.677329918$ 0.957863551 \( -\frac{2762421153954670601047049}{3515625} a^{2} + \frac{517356524035998674755129}{3515625} a + \frac{16994990990732196688324364}{3515625} \) \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 255 a^{2} - 30 a - 1607\) , \( 4253 a^{2} - 756 a - 26252\bigr] \) ${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(255a^{2}-30a-1607\right){x}+4253a^{2}-756a-26252$
15.2-b2 15.2-b 3.3.785.1 \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.677329918$ 0.957863551 \( \frac{2154621983559594094227929}{164025} a^{2} - \frac{7300914501119667671929609}{164025} a + \frac{4510427532245375321396356}{164025} \) \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( -75 a^{2} + 300 a - 277\) , \( -1077 a^{2} + 3914 a - 2954\bigr] \) ${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-75a^{2}+300a-277\right){x}-1077a^{2}+3914a-2954$
15.2-b3 15.2-b 3.3.785.1 \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $13.41863935$ 0.957863551 \( \frac{27137864062334}{50625} a^{2} - \frac{152423185980739}{50625} a + \frac{212562263704501}{50625} \) \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 10 a^{2} + 15 a - 102\) , \( 74 a^{2} + 23 a - 549\bigr] \) ${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(10a^{2}+15a-102\right){x}+74a^{2}+23a-549$
15.2-b4 15.2-b 3.3.785.1 \( 3 \cdot 5 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $107.3491148$ 0.957863551 \( \frac{140568755549}{225} a^{2} + \frac{221499293246}{225} a - \frac{272852338439}{225} \) \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 3\) , \( 2 a^{2} - 12\bigr] \) ${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+3{x}+2a^{2}-12$
15.2-b5 15.2-b 3.3.785.1 \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $429.3964592$ 0.957863551 \( -\frac{130201}{15} a^{2} - \frac{202429}{15} a + \frac{287176}{15} \) \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 8\) , \( 2 a + 1\bigr] \) ${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+8{x}+2a+1$
15.2-b6 15.2-b 3.3.785.1 \( 3 \cdot 5 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $26.83727870$ 0.957863551 \( \frac{51241969707324211486}{15} a^{2} + \frac{80745736551235585069}{15} a - \frac{99469092005530821931}{15} \) \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( -10 a^{2} - 15 a + 28\) , \( 18 a^{2} + 29 a - 47\bigr] \) ${y}^2+\left(a^{2}+a-4\right){x}{y}+{y}={x}^{3}+\left(-a^{2}+a+3\right){x}^{2}+\left(-10a^{2}-15a+28\right){x}+18a^{2}+29a-47$
15.2-c1 15.2-c 3.3.785.1 \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.057798737$ $89.22615774$ 2.761003606 \( \frac{1802836380554}{87890625} a^{2} - \frac{3740144876359}{87890625} a + \frac{2000168056831}{87890625} \) \( \bigl[1\) , \( -a^{2} + 4\) , \( a\) , \( -17 a^{2} + 55 a - 29\) , \( 108 a^{2} - 368 a + 230\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-17a^{2}+55a-29\right){x}+108a^{2}-368a+230$
15.2-c2 15.2-c 3.3.785.1 \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.115597474$ $178.4523154$ 2.761003606 \( -\frac{1859341}{9375} a^{2} - \frac{2924314}{9375} a + \frac{19868551}{9375} \) \( \bigl[1\) , \( -a^{2} + 4\) , \( a\) , \( -2 a^{2} + 5 a + 1\) , \( -2 a + 3\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a^{2}+4\right){x}^{2}+\left(-2a^{2}+5a+1\right){x}-2a+3$
  displayed columns for results

  *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.