Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
2601.1-a1 |
2601.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{6} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.2 |
$1$ |
\( 1 \) |
$3.542758762$ |
$0.739701511$ |
1.853032724 |
\( -\frac{23100424192}{14739} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( -59\) , \( -196\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}-59{x}-196$ |
2601.1-a2 |
2601.1-a |
$2$ |
$3$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{6} \cdot 17^{2} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$1$ |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$3$ |
3B.1.1 |
$1$ |
\( 3 \) |
$1.180919587$ |
$6.657313600$ |
1.853032724 |
\( \frac{32768}{459} \) |
\( \bigl[0\) , \( 1\) , \( 1\) , \( 1\) , \( -1\bigr] \) |
${y}^2+{y}={x}^{3}+{x}^{2}+{x}-1$ |
2601.1-b1 |
2601.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{4} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{3} \) |
$0.033070029$ |
$18.34402248$ |
1.715829564 |
\( -\frac{6644672}{2601} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 7 a - 11\) , \( -14 a + 20\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(7a-11\right){x}-14a+20$ |
2601.1-b2 |
2601.1-b |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{2} \cdot 17^{2} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$2$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
✓ |
|
$2$ |
2B |
$1$ |
\( 1 \) |
$0.132280117$ |
$36.68804497$ |
1.715829564 |
\( \frac{535387328}{51} \) |
\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 33 a - 50\) , \( -155 a + 220\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(33a-50\right){x}-155a+220$ |
2601.1-c1 |
2601.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{2} \cdot 17^{8} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.158409345$ |
$4.270200071$ |
1.434945077 |
\( -\frac{35905570493}{72412707} a + \frac{172936548119}{72412707} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 22 a - 27\) , \( 60 a - 84\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(22a-27\right){x}+60a-84$ |
2601.1-c2 |
2601.1-c |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{4} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.079204672$ |
$17.08080028$ |
1.434945077 |
\( -\frac{416202982}{44217} a + \frac{74095371}{4913} \) |
\( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 7 a - 12\) , \( -9 a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(7a-12\right){x}-9a+12$ |
2601.1-d1 |
2601.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{2} \cdot 17^{8} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.158409345$ |
$4.270200071$ |
1.434945077 |
\( \frac{35905570493}{72412707} a + \frac{172936548119}{72412707} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -23 a - 27\) , \( -60 a - 84\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-23a-27\right){x}-60a-84$ |
2601.1-d2 |
2601.1-d |
$2$ |
$2$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{4} \cdot 17^{4} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \cdot 3 \) |
$0.079204672$ |
$17.08080028$ |
1.434945077 |
\( \frac{416202982}{44217} a + \frac{74095371}{4913} \) |
\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( -8 a - 12\) , \( 9 a + 12\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+{x}^{2}+\left(-8a-12\right){x}+9a+12$ |
2601.1-e1 |
2601.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{4} \cdot 17^{13} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.295578960$ |
0.811609724 |
\( -\frac{6630840767433356679751}{582622237229761} a + \frac{84274075539679424994809}{5243600135067849} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -363 a - 1984\) , \( 9592 a + 35746\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-363a-1984\right){x}+9592a+35746$ |
2601.1-e2 |
2601.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{4} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.591157920$ |
0.811609724 |
\( \frac{18812414348}{3581577} a + \frac{563103442961}{32234193} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -48 a - 94\) , \( 268 a + 340\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-48a-94\right){x}+268a+340$ |
2601.1-e3 |
2601.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 17^{8} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.591157920$ |
0.811609724 |
\( \frac{44776214704960466}{217238121} a + \frac{569920783435014403}{1955143089} \) |
\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -858 a - 1309\) , \( 16954 a + 24316\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-858a-1309\right){x}+16954a+24316$ |
2601.1-e4 |
2601.1-e |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{4} \cdot 17^{7} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.295578960$ |
0.811609724 |
\( \frac{10036258969402086757063}{83521} a + \frac{127740721950153724072663}{751689} \) |
\( \bigl[1\) , \( -a\) , \( a\) , \( -2431 a + 2251\) , \( -114886 a + 178668\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-2431a+2251\right){x}-114886a+178668$ |
2601.1-f1 |
2601.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{4} \cdot 17^{7} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.295578960$ |
0.811609724 |
\( -\frac{10036258969402086757063}{83521} a + \frac{127740721950153724072663}{751689} \) |
\( \bigl[1\) , \( a\) , \( a\) , \( 2430 a + 2251\) , \( 114886 a + 178668\bigr] \) |
${y}^2+{x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(2430a+2251\right){x}+114886a+178668$ |
2601.1-f2 |
2601.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{8} \cdot 17^{8} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2Cs |
$1$ |
\( 2^{3} \) |
$1$ |
$4.591157920$ |
0.811609724 |
\( -\frac{44776214704960466}{217238121} a + \frac{569920783435014403}{1955143089} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 856 a - 1309\) , \( -16955 a + 24316\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(856a-1309\right){x}-16955a+24316$ |
2601.1-f3 |
2601.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( 3^{16} \cdot 17^{4} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$4.591157920$ |
0.811609724 |
\( -\frac{18812414348}{3581577} a + \frac{563103442961}{32234193} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 46 a - 94\) , \( -269 a + 340\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(46a-94\right){x}-269a+340$ |
2601.1-f4 |
2601.1-f |
$4$ |
$4$ |
\(\Q(\sqrt{2}) \) |
$2$ |
$[2, 0]$ |
2601.1 |
\( 3^{2} \cdot 17^{2} \) |
\( - 3^{4} \cdot 17^{13} \) |
$1.80496$ |
$(-3a-1), (3a-1), (3)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
✓ |
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$2.295578960$ |
0.811609724 |
\( \frac{6630840767433356679751}{582622237229761} a + \frac{84274075539679424994809}{5243600135067849} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 361 a - 1984\) , \( -9593 a + 35746\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(361a-1984\right){x}-9593a+35746$ |
*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.