Learn more

Refine search


Results (40 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
15.1-a1 15.1-a \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.551490810$ 2.040131471 \( \frac{5929741}{5625} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -30 a + 261\) , \( 162 a - 979\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-30a+261\right){x}+162a-979$
15.1-a2 15.1-a \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.20596324$ 2.040131471 \( \frac{205379}{75} \) \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 15 a - 54\) , \( 63 a - 313\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(15a-54\right){x}+63a-313$
15.1-b1 15.1-b \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.551490810$ 4.080262942 \( \frac{5929741}{5625} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -7 a + 43\) , \( -27 a + 197\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-7a+43\right){x}-27a+197$
15.1-b2 15.1-b \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.20596324$ 4.080262942 \( \frac{205379}{75} \) \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -2 a + 8\) , \( 9\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(-2a+8\right){x}+9$
15.1-c1 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $26.31897150$ $0.490422220$ 2.009680769 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-110{x}-880$
15.1-c2 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.644935719$ $31.38702211$ 2.009680769 \( -\frac{1}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}$
15.1-c3 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/8\Z$ $\mathrm{SU}(2)$ $13.15948575$ $1.961688882$ 2.009680769 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+35{x}-28$
15.1-c4 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $6.579742876$ $7.846755528$ 2.009680769 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-10{x}-10$
15.1-c5 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $3.289871438$ $31.38702211$ 2.009680769 \( \frac{13997521}{225} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-5{x}+2$
15.1-c6 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $13.15948575$ $1.961688882$ 2.009680769 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-135{x}-660$
15.1-c7 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $1.644935719$ $31.38702211$ 2.009680769 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-80{x}+242$
15.1-c8 15.1-c \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $26.31897150$ $0.490422220$ 2.009680769 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \) ${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}-2160{x}-39540$
15.1-d1 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.471890948$ $2.547989231$ 2.995347692 \( -\frac{147281603041}{215233605} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -990\) , \( 22765\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-990{x}+22765$
15.1-d2 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.887563793$ $10.19195692$ 2.995347692 \( -\frac{1}{15} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 0\) , \( -5\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-5$
15.1-d3 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $3.775127587$ $2.547989231$ 2.995347692 \( \frac{4733169839}{3515625} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( 315\) , \( 1066\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}+315{x}+1066$
15.1-d4 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.887563793$ $10.19195692$ 2.995347692 \( \frac{111284641}{50625} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -90\) , \( 175\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-90{x}+175$
15.1-d5 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.775127587$ $10.19195692$ 2.995347692 \( \frac{13997521}{225} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -45\) , \( -104\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-45{x}-104$
15.1-d6 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $0.943781896$ $10.19195692$ 2.995347692 \( \frac{272223782641}{164025} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -1215\) , \( 16600\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-1215{x}+16600$
15.1-d7 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $7.550255175$ $2.547989231$ 2.995347692 \( \frac{56667352321}{15} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -720\) , \( -7259\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-720{x}-7259$
15.1-d8 15.1-d \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.471890948$ $10.19195692$ 2.995347692 \( \frac{1114544804970241}{405} \) \( \bigl[1\) , \( -1\) , \( 0\) , \( -19440\) , \( 1048135\bigr] \) ${y}^2+{x}{y}={x}^{3}-{x}^{2}-19440{x}+1048135$
15.1-e1 15.1-e \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.551490810$ 4.080262942 \( \frac{5929741}{5625} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( -634 a + 4385\) , \( 17532 a - 121383\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-634a+4385\right){x}+17532a-121383$
15.1-e2 15.1-e \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.20596324$ 4.080262942 \( \frac{205379}{75} \) \( \bigl[1\) , \( 0\) , \( a + 1\) , \( 206 a - 1430\) , \( 2503 a - 17343\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(206a-1430\right){x}+2503a-17343$
15.1-f1 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $9.352879577$ $0.490422220$ 2.856692515 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12867 a - 89067\) , \( 3850257 a - 26653866\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(12867a-89067\right){x}+3850257a-26653866$
15.1-f2 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.584554973$ $31.38702211$ 2.856692515 \( -\frac{1}{15} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a + 33\) , \( -843 a + 5844\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-3a+33\right){x}-843a+5844$
15.1-f3 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $4.676439788$ $1.961688882$ 2.856692515 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -4098 a + 28383\) , \( 170895 a - 1183029\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-4098a+28383\right){x}+170895a-1183029$
15.1-f4 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $2.338219894$ $7.846755528$ 2.856692515 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1167 a - 8067\) , \( 31737 a - 219696\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(1167a-8067\right){x}+31737a-219696$
15.1-f5 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.169109947$ $31.38702211$ 2.856692515 \( \frac{13997521}{225} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 582 a - 4017\) , \( -16305 a + 112881\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(582a-4017\right){x}-16305a+112881$
15.1-f6 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $4.676439788$ $1.961688882$ 2.856692515 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 15792 a - 109317\) , \( 2820387 a - 19524471\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(15792a-109317\right){x}+2820387a-19524471$
15.1-f7 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.584554973$ $31.38702211$ 2.856692515 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 9357 a - 64767\) , \( -1200795 a + 8312646\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(9357a-64767\right){x}-1200795a+8312646$
15.1-f8 15.1-f \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $9.352879577$ $0.490422220$ 2.856692515 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 252717 a - 1749567\) , \( 176592117 a - 1222480176\bigr] \) ${y}^2+a{x}{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(252717a-1749567\right){x}+176592117a-1222480176$
15.1-g1 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.664295827$ $2.547989231$ 2.643868672 \( -\frac{147281603041}{215233605} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 1438 a - 9852\) , \( -139212 a + 963920\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1438a-9852\right){x}-139212a+963920$
15.1-g2 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/4\Z$ $\mathrm{SU}(2)$ $6.664295827$ $10.19195692$ 2.643868672 \( -\frac{1}{15} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 8 a + 48\) , \( 48 a - 120\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(8a+48\right){x}+48a-120$
15.1-g3 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $0.833036978$ $2.547989231$ 2.643868672 \( \frac{4733169839}{3515625} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( -447 a + 3198\) , \( -7386 a + 51344\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-447a+3198\right){x}-7386a+51344$
15.1-g4 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1.666073956$ $10.19195692$ 2.643868672 \( \frac{111284641}{50625} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 138 a - 852\) , \( -852 a + 6110\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(138a-852\right){x}-852a+6110$
15.1-g5 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.332147913$ $10.19195692$ 2.643868672 \( \frac{13997521}{225} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 73 a - 402\) , \( 774 a - 5146\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(73a-402\right){x}+774a-5146$
15.1-g6 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $3.332147913$ $10.19195692$ 2.643868672 \( \frac{272223782641}{164025} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 1763 a - 12102\) , \( -100302 a + 694560\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1763a-12102\right){x}-100302a+694560$
15.1-g7 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $6.664295827$ $2.547989231$ 2.643868672 \( \frac{56667352321}{15} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 1048 a - 7152\) , \( 46944 a - 324766\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(1048a-7152\right){x}+46944a-324766$
15.1-g8 15.1-g \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) $1$ $\Z/2\Z$ $\mathrm{SU}(2)$ $1.666073956$ $10.19195692$ 2.643868672 \( \frac{1114544804970241}{405} \) \( \bigl[a\) , \( a - 1\) , \( 1\) , \( 28088 a - 194352\) , \( -6474192 a + 44818500\bigr] \) ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(28088a-194352\right){x}-6474192a+44818500$
15.1-h1 15.1-h \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $6.551490810$ 2.040131471 \( \frac{5929741}{5625} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -5702 a + 39469\) , \( -473385 a + 3277047\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(-5702a+39469\right){x}-473385a+3277047$
15.1-h2 15.1-h \(\Q(\sqrt{165}) \) \( 3 \cdot 5 \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $26.20596324$ 2.040131471 \( \frac{205379}{75} \) \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 1858 a - 12866\) , \( -67602 a + 467967\bigr] \) ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(1858a-12866\right){x}-67602a+467967$
  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.