Learn more

Refine search


Results (18 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
700.2-a1 700.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.024054762$ 1.530041583 \( \frac{13113497519}{17920} a - \frac{3547675441}{8960} \) \( \bigl[1\) , \( 1\) , \( a\) , \( -29 a + 9\) , \( 46 a - 73\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-29a+9\right){x}+46a-73$
700.2-a2 700.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.674684920$ 1.530041583 \( -\frac{185012985079}{78400000} a - \frac{376583187511}{392000000} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -4 a + 123\) , \( 396 a - 51\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4a+123\right){x}+396a-51$
700.2-a3 700.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.674684920$ 1.530041583 \( \frac{9103345957169}{11239424000} a - \frac{2655632525181}{1605632000} \) \( \bigl[1\) , \( 1\) , \( a\) , \( -34 a + 104\) , \( 321 a + 134\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-34a+104\right){x}+321a+134$
700.2-a4 700.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.024054762$ 1.530041583 \( \frac{3747996503}{9175040} a + \frac{31247605623}{22937600} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( a - 12\) , \( a - 10\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(a-12\right){x}+a-10$
700.2-a5 700.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.224894973$ 1.530041583 \( -\frac{41282203518025836237719}{630503947831869440} a + \frac{37460205421439226610825}{126100789566373888} \) \( \bigl[1\) , \( 1\) , \( a\) , \( 1891 a - 421\) , \( 17926 a + 35379\bigr] \) ${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(1891a-421\right){x}+17926a+35379$
700.2-a6 700.2-a \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.224894973$ 1.530041583 \( -\frac{810722517917135481181}{23488102400} a + \frac{1861013035614760768527}{23488102400} \) \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -629 a + 10498\) , \( 294721 a - 96726\bigr] \) ${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-629a+10498\right){x}+294721a-96726$
700.2-b1 700.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.024054762$ 1.530041583 \( -\frac{13113497519}{17920} a + \frac{6018146637}{17920} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 28 a - 20\) , \( -47 a - 27\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(28a-20\right){x}-47a-27$
700.2-b2 700.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.674684920$ 1.530041583 \( \frac{185012985079}{78400000} a - \frac{650824056453}{196000000} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 4 a + 119\) , \( -396 a + 345\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(4a+119\right){x}-396a+345$
700.2-b3 700.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $0.674684920$ 1.530041583 \( -\frac{9103345957169}{11239424000} a - \frac{4743040859549}{5619712000} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 33 a + 70\) , \( -322 a + 455\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(33a+70\right){x}-322a+455$
700.2-b4 700.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/6\Z$ $\mathrm{SU}(2)$ $1$ $2.024054762$ 1.530041583 \( -\frac{3747996503}{9175040} a + \frac{81235193761}{45875200} \) \( \bigl[1\) , \( a\) , \( 0\) , \( -a - 11\) , \( -a - 9\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-a-11\right){x}-a-9$
700.2-b5 700.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.224894973$ 1.530041583 \( \frac{41282203518025836237719}{630503947831869440} a + \frac{73009411794585148408203}{315251973915934720} \) \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -1892 a + 1470\) , \( -17927 a + 53305\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-1892a+1470\right){x}-17927a+53305$
700.2-b6 700.2-b \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.224894973$ 1.530041583 \( \frac{810722517917135481181}{23488102400} a + \frac{525145258848812643673}{11744051200} \) \( \bigl[1\) , \( a\) , \( 0\) , \( 629 a + 9869\) , \( -294721 a + 197995\bigr] \) ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(629a+9869\right){x}-294721a+197995$
700.2-c1 700.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.699948933$ 2.796898497 \( -\frac{385902711}{8960} a - \frac{1290916467}{8960} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 6 a - 7\) , \( 6 a - 1\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(6a-7\right){x}+6a-1$
700.2-c2 700.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.699948933$ 2.796898497 \( \frac{385902711}{8960} a - \frac{838409589}{4480} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -6 a - 1\) , \( -6 a + 5\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+\left(-6a-1\right){x}-6a+5$
700.2-c3 700.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $3.699948933$ 2.796898497 \( \frac{1367631}{2800} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( 2\) , \( -3\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}+2{x}-3$
700.2-c4 700.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $1.849974466$ 2.796898497 \( \frac{611960049}{122500} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -18\) , \( -19\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-18{x}-19$
700.2-c5 700.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.924987233$ 2.796898497 \( \frac{74565301329}{5468750} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -88\) , \( 317\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-88{x}+317$
700.2-c6 700.2-c \(\Q(\sqrt{-7}) \) \( 2^{2} \cdot 5^{2} \cdot 7 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $0.924987233$ 2.796898497 \( \frac{2121328796049}{120050} \) \( \bigl[1\) , \( -1\) , \( 1\) , \( -268\) , \( -1619\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}-{x}^{2}-268{x}-1619$
  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.