## Results (1-50 of 80 matches)

Label Class Base field Conductor norm Rank Torsion CM Weierstrass equation
1.1-a1 1.1-a $$\Q(\sqrt{38})$$ $$1$$ $0$ $\Z/2\Z$ $-8$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-5a+15\right){x}-5a+21$
1.1-a2 1.1-a $$\Q(\sqrt{38})$$ $$1$$ $0$ $\Z/2\Z$ $-8$ ${y}^2+a{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(4a+15\right){x}+4a+21$
16.1-a1 16.1-a $$\Q(\sqrt{38})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-8$ ${y}^2={x}^{3}-a{x}^{2}+\left(-10a-49\right){x}+57a+360$
16.1-a2 16.1-a $$\Q(\sqrt{38})$$ $$2^{4}$$ $0$ $\Z/2\Z$ $-8$ ${y}^2={x}^{3}+a{x}^{2}+\left(10a-49\right){x}-57a+360$
19.1-a1 19.1-a $$\Q(\sqrt{38})$$ $$19$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(34a+219\right){x}+232a+1433$
19.1-b1 19.1-b $$\Q(\sqrt{38})$$ $$19$$ $1$ $\mathsf{trivial}$ ${y}^2+{y}={x}^{3}+{x}^{2}-769{x}-8470$
19.1-b2 19.1-b $$\Q(\sqrt{38})$$ $$19$$ $1$ $\Z/3\Z$ ${y}^2+{y}={x}^{3}+{x}^{2}-9{x}-15$
19.1-b3 19.1-b $$\Q(\sqrt{38})$$ $$19$$ $1$ $\Z/3\Z$ ${y}^2+{y}={x}^{3}+{x}^{2}+{x}$
19.1-c1 19.1-c $$\Q(\sqrt{38})$$ $$19$$ $1$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(-17a-65\right){x}-149a-876$
19.1-d1 19.1-d $$\Q(\sqrt{38})$$ $$19$$ $0$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a+1\right){x}^{2}+\left(-35a+219\right){x}-232a+1433$
19.1-e1 19.1-e $$\Q(\sqrt{38})$$ $$19$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(341584a-2105665\right){x}-269922166a+1663911967$
19.1-e2 19.1-e $$\Q(\sqrt{38})$$ $$19$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(4144a-25545\right){x}-384936a+2372892$
19.1-e3 19.1-e $$\Q(\sqrt{38})$$ $$19$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){y}={x}^{3}-{x}^{2}+\left(296a+1825\right){x}+205a+1257$
19.1-f1 19.1-f $$\Q(\sqrt{38})$$ $$19$$ $1$ $\mathsf{trivial}$ ${y}^2+a{x}{y}+{y}={x}^{3}+{x}^{2}+\left(16a-65\right){x}+149a-876$
22.1-a1 22.1-a $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-a{x}^{2}+\left(601a-3690\right){x}+22656a-139650$
22.1-b1 22.1-b $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(859a-5176\right){x}+33615a-206970$
22.1-b2 22.1-b $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $0$ $\Z/5\Z$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(14a+34\right){x}+12a+180$
22.1-c1 22.1-c $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-3a-7\right){x}+15a+87$
22.1-d1 22.1-d $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-470a-2899\right){x}+13901a+85693$
22.1-d2 22.1-d $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(5a+31\right){x}-6a-37$
22.2-a1 22.2-a $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-601a-3690\right){x}-22656a-139650$
22.2-b1 22.2-b $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $0$ $\Z/5\Z$ ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(5a+15\right){x}+3a+9$
22.2-b2 22.2-b $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $0$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+a{y}={x}^{3}+a{x}^{2}+\left(-840a-5195\right){x}-38810a-239251$
22.2-c1 22.2-c $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(2a-7\right){x}-15a+87$
22.2-d1 22.2-d $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(-5a+31\right){x}+6a-37$
22.2-d2 22.2-d $$\Q(\sqrt{38})$$ $$2 \cdot 11$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}-{x}^{2}+\left(470a-2899\right){x}-13901a+85693$
26.1-a1 26.1-a $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a+6\right){x}+a+5$
26.1-b1 26.1-b $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}-a{x}^{2}+\left(106a-642\right){x}-1260a+7760$
26.1-c1 26.1-c $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-106a-607\right){x}-1614a-9889$
26.1-d1 26.1-d $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}-a{x}^{2}+\left(80a-504\right){x}-729a+4492$
26.2-a1 26.2-a $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}+\left(a+1\right){y}={x}^{3}+\left(a-1\right){x}^{2}+6{x}-2a+5$
26.2-b1 26.2-b $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+{x}{y}={x}^{3}+a{x}^{2}+\left(-106a-642\right){x}+1260a+7760$
26.2-c1 26.2-c $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}={x}^{3}-{x}^{2}+\left(106a-607\right){x}+1614a-9889$
26.2-d1 26.2-d $$\Q(\sqrt{38})$$ $$2 \cdot 13$$ $1$ $\mathsf{trivial}$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-82a-504\right){x}+728a+4492$
32.1-a1 32.1-a $$\Q(\sqrt{38})$$ $$2^{5}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}-a{x}^{2}+11{x}-a$
32.1-b1 32.1-b $$\Q(\sqrt{38})$$ $$2^{5}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}+a{x}^{2}+\left(-740a-4549\right){x}+28481a+175560$
32.1-c1 32.1-c $$\Q(\sqrt{38})$$ $$2^{5}$$ $1$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ ${y}^2={x}^{3}-{x}$
32.1-c2 32.1-c $$\Q(\sqrt{38})$$ $$2^{5}$$ $1$ $\Z/4\Z$ $-4$ ${y}^2={x}^{3}+\left(444a+2737\right){x}$
32.1-c3 32.1-c $$\Q(\sqrt{38})$$ $$2^{5}$$ $1$ $\Z/2\Z$ $-16$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+\left(-1221a-7509\right){x}-61761a-380687$
32.1-c4 32.1-c $$\Q(\sqrt{38})$$ $$2^{5}$$ $1$ $\Z/4\Z$ $-16$ ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+\left(-1221a-7490\right){x}+53214a+328076$
32.1-d1 32.1-d $$\Q(\sqrt{38})$$ $$2^{5}$$ $0$ $\Z/2\Z$ $-4$ ${y}^2={x}^{3}+{x}$
32.1-d2 32.1-d $$\Q(\sqrt{38})$$ $$2^{5}$$ $0$ $\Z/2\Z\oplus\Z/2\Z$ $-4$ ${y}^2={x}^{3}+\left(-444a-2737\right){x}$
32.1-d3 32.1-d $$\Q(\sqrt{38})$$ $$2^{5}$$ $0$ $\Z/2\Z$ $-16$ ${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}+15{x}+22$
32.1-d4 32.1-d $$\Q(\sqrt{38})$$ $$2^{5}$$ $0$ $\Z/4\Z$ $-16$ ${y}^2+a{x}{y}={x}^{3}+{x}^{2}+34{x}+35$
32.1-e1 32.1-e $$\Q(\sqrt{38})$$ $$2^{5}$$ $0$ $\mathsf{trivial}$ ${y}^2={x}^{3}+a{x}^{2}+11{x}+a$
32.1-f1 32.1-f $$\Q(\sqrt{38})$$ $$2^{5}$$ $1$ $\mathsf{trivial}$ ${y}^2={x}^{3}-a{x}^{2}+\left(740a-4549\right){x}-28481a+175560$
34.1-a1 34.1-a $$\Q(\sqrt{38})$$ $$2 \cdot 17$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(299a-1832\right){x}-6106a+37632$
34.1-a2 34.1-a $$\Q(\sqrt{38})$$ $$2 \cdot 17$$ $0$ $\Z/2\Z$ ${y}^2+{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(4739a-29202\right){x}-430790a+2655560$
34.1-b1 34.1-b $$\Q(\sqrt{38})$$ $$2 \cdot 17$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a+8\right){x}-5a+21$
34.1-b2 34.1-b $$\Q(\sqrt{38})$$ $$2 \cdot 17$$ $1$ $\Z/2\Z$ ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-4a-2\right){x}-a-7$