| 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 |
| 304.1-a1 |
304.1-a |
$2$ |
$3$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{15} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.015217692$ |
$129.9287877$ |
1.950314167 |
\( \frac{1954327}{19} a^{2} - \frac{2781347}{38} a - \frac{6314787}{19} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 1\) , \( a^{2} - 1\) , \( 36 a^{2} - 24 a - 114\) , \( -143 a^{2} + 98 a + 459\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(36a^{2}-24a-114\right){x}-143a^{2}+98a+459$ |
| 304.1-a2 |
304.1-a |
$2$ |
$3$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{21} \cdot 19^{3} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$3$ |
3B |
$1$ |
\( 2^{2} \) |
$0.045653077$ |
$43.30959592$ |
1.950314167 |
\( -\frac{3435697639838965}{54872} a^{2} - \frac{4020062957437733}{54872} a + \frac{1583207592501673}{54872} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 1\) , \( a^{2} - 1\) , \( -74 a^{2} + 46 a + 226\) , \( -757 a^{2} + 526 a + 2441\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-74a^{2}+46a+226\right){x}-757a^{2}+526a+2441$ |
| 304.1-b1 |
304.1-b |
$1$ |
$1$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{11} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2 \) |
$1$ |
$5.390838637$ |
0.886248412 |
\( \frac{25669175664}{19} a^{2} - \frac{17683117681}{19} a - \frac{82509293055}{19} \) |
\( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( -3 a^{2} + 15 a - 3\) , \( -9 a^{2} + 31 a - 10\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-2\right){x}^{2}+\left(-3a^{2}+15a-3\right){x}-9a^{2}+31a-10$ |
| 304.1-c1 |
304.1-c |
$2$ |
$5$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{17} \cdot 19^{5} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$1.563315515$ |
1.285037438 |
\( \frac{459300992587246615484203}{4952198} a^{2} - \frac{632817728845766651512911}{9904396} a - \frac{2952680500805744366956297}{9904396} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 3\) , \( a^{2} - a - 2\) , \( -4751448 a^{2} - 5559562 a + 2189505\) , \( 10386553163 a^{2} + 12153165367 a - 4786239231\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-3\right){x}^{2}+\left(-4751448a^{2}-5559562a+2189505\right){x}+10386553163a^{2}+12153165367a-4786239231$ |
| 304.1-c2 |
304.1-c |
$2$ |
$5$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{37} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$5$ |
5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$7.816577579$ |
1.285037438 |
\( \frac{8183619}{9728} a^{2} - \frac{566281}{1216} a - \frac{23353765}{9728} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 3\) , \( a^{2} - 1\) , \( 4 a^{2} - 7 a + 1\) , \( -19 a^{2} + 50 a - 14\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a^{2}-3\right){x}^{2}+\left(4a^{2}-7a+1\right){x}-19a^{2}+50a-14$ |
| 304.1-d1 |
304.1-d |
$1$ |
$1$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{11} \cdot 19^{3} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
$1$ |
$\mathsf{trivial}$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
|
|
$1$ |
\( 2^{2} \cdot 3 \) |
$0.004946294$ |
$144.1141377$ |
2.109396335 |
\( -\frac{19944182}{6859} a^{2} - \frac{7093705}{6859} a + \frac{768959}{6859} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{2} + 2\) , \( a + 1\) , \( -6 a^{2} - 5 a + 6\) , \( 16 a^{2} + 19 a - 7\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-6a^{2}-5a+6\right){x}+16a^{2}+19a-7$ |
| 304.1-e1 |
304.1-e |
$4$ |
$6$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19^{2} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$0.526724262$ |
$34.06977672$ |
2.212651479 |
\( \frac{309847904}{361} a^{2} + \frac{362105728}{361} a - \frac{142642480}{361} \) |
\( \bigl[a^{2} - 1\) , \( a + 1\) , \( a^{2} - 1\) , \( -117 a^{2} - 136 a + 54\) , \( -1541 a^{2} - 1803 a + 710\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-117a^{2}-136a+54\right){x}-1541a^{2}-1803a+710$ |
| 304.1-e2 |
304.1-e |
$4$ |
$6$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19^{6} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 2 \) |
$1.580172787$ |
$11.35659224$ |
2.212651479 |
\( \frac{15636831814539296}{47045881} a^{2} - \frac{38648046941482112}{47045881} a + \frac{10231591814174352}{47045881} \) |
\( \bigl[a^{2} - 1\) , \( a + 1\) , \( a^{2} - 1\) , \( -287 a^{2} - 316 a + 124\) , \( 2389 a^{2} + 2745 a - 1088\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-287a^{2}-316a+124\right){x}+2389a^{2}+2745a-1088$ |
| 304.1-e3 |
304.1-e |
$4$ |
$6$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19^{3} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$3.160345575$ |
$11.35659224$ |
2.212651479 |
\( -\frac{72241514230136832}{6859} a^{2} + \frac{49766614320668672}{6859} a + \frac{232207325676879872}{6859} \) |
\( \bigl[0\) , \( a^{2} - a - 2\) , \( 0\) , \( 19 a^{2} - 59\) , \( 51 a^{2} - 24 a - 128\bigr] \) |
${y}^2={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(19a^{2}-59\right){x}+51a^{2}-24a-128$ |
| 304.1-e4 |
304.1-e |
$4$ |
$6$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 3$ |
2B, 3B |
$1$ |
\( 1 \) |
$1.053448525$ |
$34.06977672$ |
2.212651479 |
\( -\frac{16384}{19} a^{2} - \frac{319488}{19} a + \frac{737280}{19} \) |
\( \bigl[0\) , \( a^{2} - a - 2\) , \( 0\) , \( -a^{2} + 1\) , \( -a^{2}\bigr] \) |
${y}^2={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-a^{2}+1\right){x}-a^{2}$ |
| 304.1-f1 |
304.1-f |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( 2^{4} \cdot 19^{2} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$161.9155495$ |
1.663672022 |
\( \frac{1262467580748}{361} a^{2} + \frac{691215518704}{361} a - \frac{337233710396}{361} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 1\) , \( a^{2} - a - 2\) , \( -4637280672829 a^{2} - 5426019449972 a + 2136910533937\) , \( 10013891456231131020 a^{2} + 11717119071475940645 a - 4614512609495274519\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-4637280672829a^{2}-5426019449972a+2136910533937\right){x}+10013891456231131020a^{2}+11717119071475940645a-4614512609495274519$ |
| 304.1-f2 |
304.1-f |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( 2^{8} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$40.47888737$ |
1.663672022 |
\( \frac{1085233187002205994166}{19} a^{2} + \frac{1269816686949385330050}{19} a - \frac{500087528165517879840}{19} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - a - 1\) , \( a^{2} - a - 2\) , \( -74196489860904 a^{2} - 86816310141332 a + 34190568126277\) , \( 640889189198618013390 a^{2} + 749895779706018352297 a - 295328869677930514372\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-74196489860904a^{2}-86816310141332a+34190568126277\right){x}+640889189198618013390a^{2}+749895779706018352297a-295328869677930514372$ |
| 304.1-f3 |
304.1-f |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{8} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$40.47888737$ |
1.663672022 |
\( \frac{44210886365004120394}{19} a^{2} - \frac{109695799427714614146}{19} a + \frac{29848134200140905616}{19} \) |
\( \bigl[a^{2} - a - 2\) , \( a^{2} - 1\) , \( a^{2} - a - 2\) , \( -83 a^{2} - 165 a - 77\) , \( 1397 a^{2} + 1287 a - 1147\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-a-2\right){y}={x}^{3}+\left(a^{2}-1\right){x}^{2}+\left(-83a^{2}-165a-77\right){x}+1397a^{2}+1287a-1147$ |
| 304.1-f4 |
304.1-f |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{4} \cdot 19^{8} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$40.47888737$ |
1.663672022 |
\( \frac{10340474165076}{16983563041} a^{2} - \frac{8852742880880}{16983563041} a + \frac{1338218451692}{16983563041} \) |
\( \bigl[a^{2} - a - 2\) , \( -a^{2} + a + 2\) , \( a^{2} - 1\) , \( -18160617495444906177336 a^{2} - 21249493120204410252900 a + 8368614618526255000989\) , \( -536959447312769742344605636255269 a^{2} - 628288993166855612489020976496062 a + 247436888171039421932412622008483\bigr] \) |
${y}^2+\left(a^{2}-a-2\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+a+2\right){x}^{2}+\left(-18160617495444906177336a^{2}-21249493120204410252900a+8368614618526255000989\right){x}-536959447312769742344605636255269a^{2}-628288993166855612489020976496062a+247436888171039421932412622008483$ |
| 304.1-f5 |
304.1-f |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( 2^{4} \cdot 19^{2} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2 \) |
$1$ |
$161.9155495$ |
1.663672022 |
\( -\frac{2600685531200}{361} a^{2} + \frac{1791591929856}{361} a + \frac{8359434846528}{361} \) |
\( \bigl[a^{2} - 1\) , \( a^{2} - a - 2\) , \( a + 1\) , \( -58064080861080878229680196 a^{2} - 67939996373912051666365728 a + 26756574550794359564920683\) , \( 4314407368877525168466506062412433615319 a^{2} + 5048229760123373695144287982872042194162 a - 1988126922805458487047615522995940613193\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-2\right){x}^{2}+\left(-58064080861080878229680196a^{2}-67939996373912051666365728a+26756574550794359564920683\right){x}+4314407368877525168466506062412433615319a^{2}+5048229760123373695144287982872042194162a-1988126922805458487047615522995940613193$ |
| 304.1-f6 |
304.1-f |
$6$ |
$8$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( 2^{8} \cdot 19^{4} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2 \) |
$1$ |
$161.9155495$ |
1.663672022 |
\( -\frac{2121702304}{130321} a^{2} + \frac{4240273184}{130321} a + \frac{19173819072}{130321} \) |
\( \bigl[a^{2} - 1\) , \( a + 1\) , \( 0\) , \( -928367100192790709072 a^{2} - 1086269798563781515080 a + 427801889885126126429\) , \( 28191044080317044316522615572325 a^{2} + 32985959722257816422718679442715 a - 12990746799288808960892463700085\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-928367100192790709072a^{2}-1086269798563781515080a+427801889885126126429\right){x}+28191044080317044316522615572325a^{2}+32985959722257816422718679442715a-12990746799288808960892463700085$ |
| 304.1-g1 |
304.1-g |
$4$ |
$10$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19^{10} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 2 \cdot 5 \) |
$1$ |
$10.04691768$ |
2.064628865 |
\( \frac{34600248516351310880}{6131066257801} a^{2} + \frac{14707001073639931296}{6131066257801} a - \frac{7931450838072839760}{6131066257801} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2\) , \( a^{2} - 1\) , \( -1037279 a^{2} - 1213704 a + 477990\) , \( 1059093688 a^{2} + 1239231212 a - 488042156\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2\right){x}^{2}+\left(-1037279a^{2}-1213704a+477990\right){x}+1059093688a^{2}+1239231212a-488042156$ |
| 304.1-g2 |
304.1-g |
$4$ |
$10$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19^{2} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 2 \) |
$1$ |
$50.23458840$ |
2.064628865 |
\( \frac{19422176}{361} a^{2} - \frac{29688224}{361} a + \frac{7279536}{361} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 3\) , \( 0\) , \( -a^{2} + 1\) , \( -2 a^{2} + 3\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}={x}^{3}+\left(-a^{2}+3\right){x}^{2}+\left(-a^{2}+1\right){x}-2a^{2}+3$ |
| 304.1-g3 |
304.1-g |
$4$ |
$10$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.1 |
$1$ |
\( 1 \) |
$1$ |
$100.4691768$ |
2.064628865 |
\( -\frac{2985984}{19} a^{2} + \frac{2048000}{19} a + \frac{9617408}{19} \) |
\( \bigl[0\) , \( -a\) , \( 0\) , \( -27907 a^{2} - 32654 a + 12860\) , \( -97420996 a^{2} - 113990991 a + 44892679\bigr] \) |
${y}^2={x}^{3}-a{x}^{2}+\left(-27907a^{2}-32654a+12860\right){x}-97420996a^{2}-113990991a+44892679$ |
| 304.1-g4 |
304.1-g |
$4$ |
$10$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{12} \cdot 19^{5} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2, 5$ |
2B, 5B.4.2 |
$1$ |
\( 5 \) |
$1$ |
$20.09383536$ |
2.064628865 |
\( \frac{21475865428001583104}{2476099} a^{2} - \frac{53285799291084800000}{2476099} a + \frac{14499029076062806016}{2476099} \) |
\( \bigl[0\) , \( -a^{2} + 2 a + 3\) , \( 0\) , \( -165965341312 a^{2} - 194193803116 a + 76478676008\) , \( 79041132025753191 a^{2} + 92484960470958028 a - 36423033143090658\bigr] \) |
${y}^2={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-165965341312a^{2}-194193803116a+76478676008\right){x}+79041132025753191a^{2}+92484960470958028a-36423033143090658$ |
| 304.1-h1 |
304.1-h |
$4$ |
$4$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{4} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 1 \) |
$1$ |
$80.67147390$ |
1.657788576 |
\( \frac{40162624}{19} a^{2} + \frac{46999296}{19} a - \frac{18475072}{19} \) |
\( \bigl[a^{2} - 1\) , \( 1\) , \( a + 1\) , \( -6205474271517103 a^{2} - 7260941588207693 a + 2859551593800824\) , \( -490167215624362322704696 a^{2} - 573538035189175612908745 a + 225874507143010365778663\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-6205474271517103a^{2}-7260941588207693a+2859551593800824\right){x}-490167215624362322704696a^{2}-573538035189175612908745a+225874507143010365778663$ |
| 304.1-h2 |
304.1-h |
$4$ |
$4$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( 2^{8} \cdot 19^{2} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z\oplus\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2Cs |
$1$ |
\( 2^{2} \) |
$1$ |
$80.67147390$ |
1.657788576 |
\( -\frac{59051232}{361} a^{2} + \frac{40903584}{361} a + \frac{190979584}{361} \) |
\( \bigl[a^{2} - 1\) , \( -a^{2} + 2 a + 3\) , \( a^{2} - 1\) , \( -2466010225 a^{2} - 2885445238 a + 1136364955\) , \( -96944702174508 a^{2} - 113433685964376 a + 44673197484049\bigr] \) |
${y}^2+\left(a^{2}-1\right){x}{y}+\left(a^{2}-1\right){y}={x}^{3}+\left(-a^{2}+2a+3\right){x}^{2}+\left(-2466010225a^{2}-2885445238a+1136364955\right){x}-96944702174508a^{2}-113433685964376a+44673197484049$ |
| 304.1-h3 |
304.1-h |
$4$ |
$4$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{4} \cdot 19^{4} \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$1$ |
\( 2^{2} \) |
$1$ |
$80.67147390$ |
1.657788576 |
\( \frac{41101257644}{130321} a^{2} - \frac{100894122520}{130321} a + \frac{27381525980}{130321} \) |
\( \bigl[a + 1\) , \( a^{2} - a - 1\) , \( a + 1\) , \( -150880121110 a^{2} - 176542790813 a + 69527238679\) , \( 55344181804017466 a^{2} + 64757479242255261 a - 25503214800468369\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a^{2}-a-1\right){x}^{2}+\left(-150880121110a^{2}-176542790813a+69527238679\right){x}+55344181804017466a^{2}+64757479242255261a-25503214800468369$ |
| 304.1-h4 |
304.1-h |
$4$ |
$4$ |
3.3.148.1 |
$3$ |
$[3, 0]$ |
304.1 |
\( 2^{4} \cdot 19 \) |
\( - 2^{4} \cdot 19 \) |
$2.81891$ |
$(a^2-a-2), (-a^2-a-1)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
|
|
|
|
$2$ |
2B |
$4$ |
\( 1 \) |
$1$ |
$20.16786847$ |
1.657788576 |
\( -\frac{1710639227076}{19} a^{2} + \frac{1178445717064}{19} a + \frac{5498542045596}{19} \) |
\( \bigl[a + 1\) , \( -a^{2} + 2 a + 2\) , \( a + 1\) , \( 3 a^{2} + a - 4\) , \( 2 a^{2} - 3 a - 9\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a^{2}+2a+2\right){x}^{2}+\left(3a^{2}+a-4\right){x}+2a^{2}-3a-9$ |
*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.
