| 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 |
| 100.1-a1 |
100.1-a |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$16.70104037$ |
2.231770395 |
\( \frac{8192}{5} \) |
\( \bigl[0\) , \( a - 1\) , \( a\) , \( 2 a + 15\) , \( 2 a\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a+15\right){x}+2a$ |
| 100.1-b1 |
100.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{10} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$13.68379308$ |
1.828573766 |
\( -\frac{1158666707968}{78125} a - \frac{4335608761344}{78125} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -2061 a - 7707\) , \( 95949 a + 359003\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-2061a-7707\right){x}+95949a+359003$ |
| 100.1-b2 |
100.1-b |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{22} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.520421453$ |
1.828573766 |
\( -\frac{92684247952980992}{476837158203125} a + \frac{317890193866097664}{476837158203125} \) |
\( \bigl[0\) , \( a\) , \( a\) , \( -1051 a - 3927\) , \( 193543 a + 724165\bigr] \) |
${y}^2+a{y}={x}^{3}+a{x}^{2}+\left(-1051a-3927\right){x}+193543a+724165$ |
| 100.1-c1 |
100.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{10} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$0.873413917$ |
2.451011725 |
\( \frac{1158666707968}{78125} a - \frac{4335608761344}{78125} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -11 a - 58\) , \( -55 a - 231\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-11a-58\right){x}-55a-231$ |
| 100.1-c2 |
100.1-c |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{22} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$0.873413917$ |
2.451011725 |
\( \frac{92684247952980992}{476837158203125} a + \frac{317890193866097664}{476837158203125} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 99 a + 362\) , \( 473 a + 1715\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(99a+362\right){x}+473a+1715$ |
| 100.1-d1 |
100.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{10} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\Z/3\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.1 |
$1$ |
\( 3^{2} \) |
$1$ |
$13.68379308$ |
1.828573766 |
\( \frac{1158666707968}{78125} a - \frac{4335608761344}{78125} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 2061 a - 7707\) , \( -95949 a + 359003\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(2061a-7707\right){x}-95949a+359003$ |
| 100.1-d2 |
100.1-d |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{22} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B.1.2 |
$9$ |
\( 1 \) |
$1$ |
$1.520421453$ |
1.828573766 |
\( \frac{92684247952980992}{476837158203125} a + \frac{317890193866097664}{476837158203125} \) |
\( \bigl[0\) , \( -a\) , \( a\) , \( 1051 a - 3927\) , \( -193543 a + 724165\bigr] \) |
${y}^2+a{y}={x}^{3}-a{x}^{2}+\left(1051a-3927\right){x}-193543a+724165$ |
| 100.1-e1 |
100.1-e |
$1$ |
$1$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{2} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
|
|
$1$ |
\( 1 \) |
$1$ |
$16.70104037$ |
2.231770395 |
\( \frac{8192}{5} \) |
\( \bigl[0\) , \( -a - 1\) , \( a\) , \( -2 a + 15\) , \( -2 a\bigr] \) |
${y}^2+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-2a+15\right){x}-2a$ |
| 100.1-f1 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 2^{2} \) |
$6.683774655$ |
$1.772687765$ |
3.166576821 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -1093 a - 4067\) , \( -57781 a - 216176\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-1093a-4067\right){x}-57781a-216176$ |
| 100.1-f2 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 2^{2} \cdot 3 \) |
$2.227924885$ |
$15.95418988$ |
3.166576821 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -107 a + 423\) , \( -1257 a + 4724\bigr] \) |
${y}^2+a{x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-107a+423\right){x}-1257a+4724$ |
| 100.1-f3 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/6\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.1 |
$1$ |
\( 3 \) |
$4.455849770$ |
$31.90837977$ |
3.166576821 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-{x}$ |
| 100.1-f4 |
100.1-f |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B.1.2 |
$1$ |
\( 1 \) |
$13.36754931$ |
$3.545375530$ |
3.166576821 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \) |
${y}^2={x}^{3}+{x}^{2}-41{x}-116$ |
| 100.1-g1 |
100.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{10} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$0.873413917$ |
2.451011725 |
\( -\frac{1158666707968}{78125} a - \frac{4335608761344}{78125} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( 11 a - 58\) , \( 55 a - 231\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(11a-58\right){x}+55a-231$ |
| 100.1-g2 |
100.1-g |
$2$ |
$3$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{22} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 3 \cdot 7 \) |
$1$ |
$0.873413917$ |
2.451011725 |
\( -\frac{92684247952980992}{476837158203125} a + \frac{317890193866097664}{476837158203125} \) |
\( \bigl[0\) , \( -1\) , \( a\) , \( -99 a + 362\) , \( -473 a + 1715\bigr] \) |
${y}^2+a{y}={x}^{3}-{x}^{2}+\left(-99a+362\right){x}-473a+1715$ |
| 100.1-h1 |
100.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{12} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3^{2} \) |
$0.137812304$ |
$10.34365470$ |
3.428786956 |
\( -\frac{20720464}{15625} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( -7\) , \( 9\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}-7{x}+9$ |
| 100.1-h2 |
100.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{4} \cdot 5^{4} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2^{2} \cdot 3 \) |
$0.413436914$ |
$10.34365470$ |
3.428786956 |
\( \frac{21296}{25} \) |
\( \bigl[a\) , \( -1\) , \( 0\) , \( 3\) , \( 1\bigr] \) |
${y}^2+a{x}{y}={x}^{3}-{x}^{2}+3{x}+1$ |
| 100.1-h3 |
100.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{2} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3 \) |
$0.826873828$ |
$20.68730941$ |
3.428786956 |
\( \frac{16384}{5} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -160 a - 594\) , \( -1266 a - 4735\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-160a-594\right){x}-1266a-4735$ |
| 100.1-h4 |
100.1-h |
$4$ |
$6$ |
\(\Q(\sqrt{14}) \) |
$2$ |
$[2, 0]$ |
100.1 |
\( 2^{2} \cdot 5^{2} \) |
\( 2^{8} \cdot 5^{6} \) |
$2.11462$ |
$(-a+4), (-a+3), (-a-3)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 3^{2} \) |
$0.275624609$ |
$20.68730941$ |
3.428786956 |
\( \frac{488095744}{125} \) |
\( \bigl[0\) , \( a\) , \( 0\) , \( 4960 a - 18554\) , \( -373910 a + 1399045\bigr] \) |
${y}^2={x}^{3}+a{x}^{2}+\left(4960a-18554\right){x}-373910a+1399045$ |
*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.
