Elliptic curves over Q(−7)\Q(\sqrt{-7})

Results (1-50 of 70927 matches)

  Download displayed columns for results to

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
16.1-CMa1	16.1-CMa	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{12}$	$0.47284$	$(a)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{yes}$	$-7$	$\mathrm{U}(1)$	✓			✓			$1$	$2^{2}$	$1$	$6.540964764$	0.309031537	$-3375$	$\bigl[a$ , $-a - 1$ , $0$ , $1$ , $0\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+{x}$
16.1-CMa2	16.1-CMa	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	16.1	$2^{4}$	$2^{12}$	$0.47284$	$(a)$	0	$\Z/4\Z$	$\textsf{yes}$	$-28$	$\mathrm{U}(1)$	✓			✓			$1$	$2$	$1$	$3.270482382$	0.309031537	$16581375$	$\bigl[a$ , $-a - 1$ , $0$ , $-15 a + 11$ , $-7 a + 26\bigr]$	${y}^2+a{x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-15a+11\right){x}-7a+26$
16.5-CMa1	16.5-CMa	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	16.5	$2^{4}$	$2^{12}$	$0.47284$	$(-a+1)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{yes}$	$-7$	$\mathrm{U}(1)$	✓			✓			$1$	$2^{2}$	$1$	$6.540964764$	0.309031537	$-3375$	$\bigl[a + 1$ , $1$ , $a + 1$ , $0$ , $0\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}$
16.5-CMa2	16.5-CMa	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	16.5	$2^{4}$	$2^{12}$	$0.47284$	$(-a+1)$	0	$\Z/4\Z$	$\textsf{yes}$	$-28$	$\mathrm{U}(1)$	✓			✓			$1$	$2$	$1$	$3.270482382$	0.309031537	$16581375$	$\bigl[a + 1$ , $1$ , $a + 1$ , $15 a - 5$ , $22 a + 14\bigr]$	${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(15a-5\right){x}+22a+14$
28.2-a1	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{36} \cdot 7^{2}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cs, 3B.1.2	$1$	$2^{3}$	$1$	$0.875417135$	0.330876576	$-\frac{548347731625}{1835008}$	$\bigl[1$ , $0$ , $1$ , $-171$ , $-874\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-171{x}-874$
28.2-a2	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{15} \cdot 7^{3}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Cs.1.1	$1$	$2 \cdot 3$	$1$	$2.626251405$	0.330876576	$-\frac{10538337875}{200704} a - \frac{13018580375}{100352}$	$\bigl[1$ , $a$ , $a + 1$ , $-10 a + 15$ , $-5 a - 16\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(-10a+15\right){x}-5a-16$
28.2-a3	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{15} \cdot 7^{3}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3Cs.1.1	$1$	$2 \cdot 3$	$1$	$2.626251405$	0.330876576	$\frac{10538337875}{200704} a - \frac{36575498625}{200704}$	$\bigl[1$ , $-a + 1$ , $a$ , $9 a + 6$ , $4 a - 20\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9a+6\right){x}+4a-20$
28.2-a4	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{5} \cdot 7$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.1	$1$	$2$	$1$	$7.878754216$	0.330876576	$-\frac{831875}{112} a - \frac{166375}{112}$	$\bigl[1$ , $-a + 1$ , $a$ , $-a + 1$ , $-a + 1\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+1\right){x}-a+1$
28.2-a5	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{5} \cdot 7$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.1	$1$	$2$	$1$	$7.878754216$	0.330876576	$\frac{831875}{112} a - \frac{499125}{56}$	$\bigl[1$ , $a$ , $a + 1$ , $0$ , $0\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}$
28.2-a6	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{4} \cdot 7^{2}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cs, 3B.1.1	$1$	$2^{3}$	$1$	$7.878754216$	0.330876576	$-\frac{15625}{28}$	$\bigl[1$ , $0$ , $1$ , $-1$ , $0\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-{x}$
28.2-a7	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{12} \cdot 7^{6}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2Cs, 3Cs.1.1	$1$	$2^{3} \cdot 3$	$1$	$2.626251405$	0.330876576	$\frac{9938375}{21952}$	$\bigl[1$ , $0$ , $1$ , $4$ , $-6\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+4{x}-6$
28.2-a8	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{45} \cdot 7$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.2	$1$	$2$	$1$	$0.875417135$	0.330876576	$-\frac{70135314719125}{481036337152} a + \frac{179276652423375}{240518168576}$	$\bigl[1$ , $a$ , $a + 1$ , $30 a - 40$ , $-30 a - 154\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+a{x}^{2}+\left(30a-40\right){x}-30a-154$
28.2-a9	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{45} \cdot 7$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓		✓		$2, 3$	2B, 3B.1.2	$1$	$2$	$1$	$0.875417135$	0.330876576	$\frac{70135314719125}{481036337152} a + \frac{288417990127625}{481036337152}$	$\bigl[1$ , $-a + 1$ , $a$ , $-31 a - 9$ , $29 a - 183\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-31a-9\right){x}+29a-183$
28.2-a10	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{6} \cdot 7^{12}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3Cs.1.1	$1$	$2^{2} \cdot 3$	$1$	$1.313125702$	0.330876576	$\frac{4956477625}{941192}$	$\bigl[1$ , $0$ , $1$ , $-36$ , $-70\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-36{x}-70$
28.2-a11	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{2} \cdot 7^{4}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2}$	$1$	$3.939377108$	0.330876576	$\frac{128787625}{98}$	$\bigl[1$ , $0$ , $1$ , $-11$ , $12\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-11{x}+12$
28.2-a12	28.2-a	$12$	$36$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	28.2	$2^{2} \cdot 7$	$2^{18} \cdot 7^{4}$	$0.54385$	$(a), (-a+1), (-2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$0.437708567$	0.330876576	$\frac{2251439055699625}{25088}$	$\bigl[1$ , $0$ , $1$ , $-2731$ , $-55146\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}-2731{x}-55146$
44.3-a1	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{10} \cdot 11^{3}$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{3}$	$1$	$1.680888225$	0.635316032	$\frac{2775668240489}{85184} a - \frac{3929396676037}{42592}$	$\bigl[1$ , $a$ , $0$ , $-55 a + 91$ , $87 a + 359\bigr]$	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-55a+91\right){x}+87a+359$
44.3-a2	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{7} \cdot 11^{12}$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$0.840444112$	0.635316032	$-\frac{41728910180660407}{200859416110144} a - \frac{5044929390482523}{100429708055072}$	$\bigl[1$ , $1$ , $a + 1$ , $-4 a + 40$ , $135 a + 83\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-4a+40\right){x}+135a+83$
44.3-a3	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{14} \cdot 11$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/12\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3$	$1$	$5.042664675$	0.635316032	$\frac{2222449}{45056} a + \frac{42043605}{45056}$	$\bigl[1$ , $a$ , $0$ , $1$ , $1\bigr]$	${y}^2+{x}{y}={x}^{3}+a{x}^{2}+{x}+1$
44.3-a4	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{25} \cdot 11^{3}$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2$	$1$	$1.680888225$	0.635316032	$-\frac{74168468086089}{22330474496} a + \frac{45400743717419}{11165237248}$	$\bigl[1$ , $-a + 1$ , $1$ , $14 a - 17$ , $-19 a + 5\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(14a-17\right){x}-19a+5$
44.3-a5	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{10} \cdot 11^{2}$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B.1.1	$1$	$2^{3} \cdot 3$	$1$	$5.042664675$	0.635316032	$-\frac{998361}{7744} a + \frac{23448551}{7744}$	$\bigl[1$ , $1$ , $a + 1$ , $a$ , $1\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+a{x}+1$
44.3-a6	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{14} \cdot 11^{6}$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B.1.2	$1$	$2^{3}$	$1$	$1.680888225$	0.635316032	$\frac{49453830610989}{7256313856} a - \frac{991801247255}{3628156928}$	$\bigl[1$ , $1$ , $a + 1$ , $-14 a - 10$ , $27 a - 9\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+\left(-14a-10\right){x}+27a-9$
44.3-a7	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{11} \cdot 11$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2 \cdot 3$	$1$	$5.042664675$	0.635316032	$\frac{7153263}{2816} a + \frac{40910099}{1408}$	$\bigl[1$ , $-a + 1$ , $1$ , $-a + 3$ , $-3 a + 1\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-a+3\right){x}-3a+1$
44.3-a8	44.3-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.3	$2^{2} \cdot 11$	$2^{5} \cdot 11^{4}$	$0.60891$	$(a), (-a+1), (-2a+3)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2} \cdot 3$	$1$	$2.521332337$	0.635316032	$-\frac{67333244623}{117128} a + \frac{557731279327}{117128}$	$\bigl[1$ , $1$ , $a + 1$ , $21 a$ , $20 a + 57\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+{x}^{2}+21a{x}+20a+57$
44.4-a1	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{10} \cdot 11^{3}$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{3}$	$1$	$1.680888225$	0.635316032	$-\frac{2775668240489}{85184} a - \frac{5083125111585}{85184}$	$\bigl[1$ , $-a + 1$ , $0$ , $55 a + 36$ , $-87 a + 446\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(55a+36\right){x}-87a+446$
44.4-a2	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{7} \cdot 11^{12}$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2^{2}$	$1$	$0.840444112$	0.635316032	$\frac{41728910180660407}{200859416110144} a - \frac{51818768961625453}{200859416110144}$	$\bigl[1$ , $1$ , $a$ , $3 a + 37$ , $-136 a + 219\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(3a+37\right){x}-136a+219$
44.4-a3	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{14} \cdot 11$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/12\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{3} \cdot 3$	$1$	$5.042664675$	0.635316032	$-\frac{2222449}{45056} a + \frac{22133027}{22528}$	$\bigl[1$ , $-a + 1$ , $0$ , $1$ , $1\bigr]$	${y}^2+{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+{x}+1$
44.4-a4	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{25} \cdot 11^{3}$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.2	$1$	$2$	$1$	$1.680888225$	0.635316032	$\frac{74168468086089}{22330474496} a + \frac{16633019348749}{22330474496}$	$\bigl[1$ , $a$ , $1$ , $-14 a - 3$ , $19 a - 14\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(-14a-3\right){x}+19a-14$
44.4-a5	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{10} \cdot 11^{2}$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B.1.1	$1$	$2^{3} \cdot 3$	$1$	$5.042664675$	0.635316032	$\frac{998361}{7744} a + \frac{11225095}{3872}$	$\bigl[1$ , $1$ , $a$ , $-2 a + 2$ , $-a + 2\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-2a+2\right){x}-a+2$
44.4-a6	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{14} \cdot 11^{6}$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2Cs, 3B.1.2	$1$	$2^{3}$	$1$	$1.680888225$	0.635316032	$-\frac{49453830610989}{7256313856} a + \frac{47470228116479}{7256313856}$	$\bigl[1$ , $1$ , $a$ , $13 a - 23$ , $-28 a + 19\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(13a-23\right){x}-28a+19$
44.4-a7	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{11} \cdot 11$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2 \cdot 3$	$1$	$5.042664675$	0.635316032	$-\frac{7153263}{2816} a + \frac{88973461}{2816}$	$\bigl[1$ , $a$ , $1$ , $a + 2$ , $3 a - 2\bigr]$	${y}^2+{x}{y}+{y}={x}^{3}+a{x}^{2}+\left(a+2\right){x}+3a-2$
44.4-a8	44.4-a	$8$	$12$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	44.4	$2^{2} \cdot 11$	$2^{5} \cdot 11^{4}$	$0.60891$	$(a), (-a+1), (2a+1)$	0	$\Z/6\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2, 3$	2B, 3B.1.1	$1$	$2^{2} \cdot 3$	$1$	$2.521332337$	0.635316032	$\frac{67333244623}{117128} a + \frac{61299754338}{14641}$	$\bigl[1$ , $1$ , $a$ , $-22 a + 22$ , $-21 a + 78\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-22a+22\right){x}-21a+78$
46.2-a1	46.2-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.2	$2 \cdot 23$	$2^{2} \cdot 23$	$0.61571$	$(a), (2a+3)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$6.500075531$	0.614199405	$-\frac{13982353}{92} a - \frac{23126489}{92}$	$\bigl[1$ , $-a - 1$ , $a + 1$ , $-4$ , $-1\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}-4{x}-1$
46.2-a2	46.2-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.2	$2 \cdot 23$	$2^{2} \cdot 23^{4}$	$0.61571$	$(a), (2a+3)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{2}$	$1$	$3.250037765$	0.614199405	$\frac{77942691519}{1119364} a - \frac{145858368769}{1119364}$	$\bigl[1$ , $-a$ , $a$ , $-6 a + 10$ , $2 a + 8\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-6a+10\right){x}+2a+8$
46.2-a3	46.2-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.2	$2 \cdot 23$	$2 \cdot 23^{8}$	$0.61571$	$(a), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$1.625018882$	0.614199405	$\frac{5221695638593}{156621970562} a + \frac{45422616717183}{156621970562}$	$\bigl[1$ , $-a$ , $a$ , $-a + 10$ , $-8 a + 30\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-a+10\right){x}-8a+30$
46.2-a4	46.2-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.2	$2 \cdot 23$	$2^{4} \cdot 23^{2}$	$0.61571$	$(a), (2a+3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{3}$	$1$	$6.500075531$	0.614199405	$-\frac{1695309}{8464} a + \frac{8874095}{8464}$	$\bigl[1$ , $-a$ , $a$ , $-a$ , $0\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-a{x}$
46.2-a5	46.2-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.2	$2 \cdot 23$	$2^{8} \cdot 23$	$0.61571$	$(a), (2a+3)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3}$	$1$	$6.500075531$	0.614199405	$\frac{2993221}{5888} a + \frac{15291513}{5888}$	$\bigl[1$ , $a - 1$ , $a + 1$ , $-a - 2$ , $-a + 1\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-a-2\right){x}-a+1$
46.2-a6	46.2-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.2	$2 \cdot 23$	$2 \cdot 23^{2}$	$0.61571$	$(a), (2a+3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$1.625018882$	0.614199405	$-\frac{14178949136401}{1058} a + \frac{7909975811569}{1058}$	$\bigl[1$ , $-a$ , $a$ , $-91 a + 170$ , $240 a + 618\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}+\left(-91a+170\right){x}+240a+618$
46.3-a1	46.3-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.3	$2 \cdot 23$	$2^{2} \cdot 23$	$0.61571$	$(-a+1), (-2a+5)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$6.500075531$	0.614199405	$\frac{13982353}{92} a - \frac{18554421}{46}$	$\bigl[1$ , $a + 1$ , $a + 1$ , $a - 4$ , $-a - 4\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(a-4\right){x}-a-4$
46.3-a2	46.3-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.3	$2 \cdot 23$	$2^{2} \cdot 23^{4}$	$0.61571$	$(-a+1), (-2a+5)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{2}$	$1$	$3.250037765$	0.614199405	$-\frac{77942691519}{1119364} a - \frac{33957838625}{559682}$	$\bigl[1$ , $a - 1$ , $a + 1$ , $5 a + 4$ , $-3 a + 10\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(5a+4\right){x}-3a+10$
46.3-a3	46.3-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.3	$2 \cdot 23$	$2 \cdot 23^{8}$	$0.61571$	$(-a+1), (-2a+5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$1.625018882$	0.614199405	$-\frac{5221695638593}{156621970562} a + \frac{25322156177888}{78310985281}$	$\bigl[1$ , $a - 1$ , $a + 1$ , $9$ , $7 a + 22\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+9{x}+7a+22$
46.3-a4	46.3-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.3	$2 \cdot 23$	$2^{4} \cdot 23^{2}$	$0.61571$	$(-a+1), (-2a+5)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2Cs	$1$	$2^{3}$	$1$	$6.500075531$	0.614199405	$\frac{1695309}{8464} a + \frac{3589393}{4232}$	$\bigl[1$ , $a - 1$ , $a + 1$ , $-1$ , $-a\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}-{x}-a$
46.3-a5	46.3-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.3	$2 \cdot 23$	$2^{8} \cdot 23$	$0.61571$	$(-a+1), (-2a+5)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2^{3}$	$1$	$6.500075531$	0.614199405	$-\frac{2993221}{5888} a + \frac{9142367}{2944}$	$\bigl[1$ , $-a$ , $a$ , $-2$ , $1\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}-a{x}^{2}-2{x}+1$
46.3-a6	46.3-a	$6$	$8$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	46.3	$2 \cdot 23$	$2 \cdot 23^{2}$	$0.61571$	$(-a+1), (-2a+5)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$			✓		$2$	2B	$1$	$2$	$1$	$1.625018882$	0.614199405	$\frac{14178949136401}{1058} a - \frac{3134486662416}{529}$	$\bigl[1$ , $a - 1$ , $a + 1$ , $90 a + 79$ , $-241 a + 858\bigr]$	${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+\left(90a+79\right){x}-241a+858$
49.1-CMa1	49.1-CMa	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	49.1	$7^{2}$	$7^{6}$	$0.62551$	$(-2a+1)$	0	$\Z/2\Z\oplus\Z/2\Z$	$\textsf{yes}$	$-7$	$\mathrm{U}(1)$	✓	✓		✓	$7$	7B.1.4[2]	$1$	$2^{2}$	$1$	$4.944504600$	0.934423537	$-3375$	$\bigl[1$ , $-1$ , $0$ , $-2$ , $-1\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}-2{x}-1$
49.1-CMa2	49.1-CMa	$2$	$2$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	49.1	$7^{2}$	$7^{6}$	$0.62551$	$(-2a+1)$	0	$\Z/2\Z$	$\textsf{yes}$	$-28$	$\mathrm{U}(1)$	✓	✓		✓	$7$	7B.1.4[2]	$1$	$2$	$1$	$2.472252300$	0.934423537	$16581375$	$\bigl[1$ , $-1$ , $0$ , $-37$ , $-78\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}-37{x}-78$
63.1-a1	63.1-a	$8$	$16$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	63.1	$3^{2} \cdot 7$	$3^{2} \cdot 7^{16}$	$0.66607$	$(-2a+1), (3)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2$	$1$	$0.862076929$	0.325834452	$-\frac{4354703137}{17294403}$	$\bigl[1$ , $0$ , $0$ , $-34$ , $-217\bigr]$	${y}^2+{x}{y}={x}^{3}-34{x}-217$
63.1-a2	63.1-a	$8$	$16$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	63.1	$3^{2} \cdot 7$	$3^{4} \cdot 7^{2}$	$0.66607$	$(-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{2}$	$1$	$6.896615437$	0.325834452	$\frac{103823}{63}$	$\bigl[1$ , $0$ , $0$ , $1$ , $0\bigr]$	${y}^2+{x}{y}={x}^{3}+{x}$
63.1-a3	63.1-a	$8$	$16$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	63.1	$3^{2} \cdot 7$	$3^{8} \cdot 7^{4}$	$0.66607$	$(-2a+1), (3)$	0	$\Z/2\Z\oplus\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2Cs	$1$	$2^{3}$	$1$	$3.448307718$	0.325834452	$\frac{7189057}{3969}$	$\bigl[1$ , $0$ , $0$ , $-4$ , $-1\bigr]$	${y}^2+{x}{y}={x}^{3}-4{x}-1$
63.1-a4	63.1-a	$8$	$16$	$\Q(\sqrt{-7})$	$2$	$[0, 1]$	63.1	$3^{2} \cdot 7$	$3^{16} \cdot 7^{2}$	$0.66607$	$(-2a+1), (3)$	0	$\Z/8\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{4}$	$1$	$1.724153859$	0.325834452	$\frac{6570725617}{45927}$	$\bigl[1$ , $0$ , $0$ , $-39$ , $90\bigr]$	${y}^2+{x}{y}={x}^{3}-39{x}+90$

  Download displayed columns for results to

  *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.