## Refine search

*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.

## Results (1-50 of 88 matches)

Label Base field Conductor Isogeny class Weierstrass coefficients
16.1-a1 $$\Q(\sqrt{21})$$ 16.1 16.1-a $$\bigl[0$$ , $$-a - 1$$ , $$0$$ , $$a + 2$$ , $$-2\bigr]$$
16.1-a2 $$\Q(\sqrt{21})$$ 16.1 16.1-a $$\bigl[0$$ , $$a + 1$$ , $$0$$ , $$a + 2$$ , $$0\bigr]$$
25.2-b1 $$\Q(\sqrt{21})$$ 25.2 25.2-b $$\bigl[0$$ , $$a + 1$$ , $$a + 1$$ , $$a + 2$$ , $$-2 a + 4\bigr]$$
25.2-b2 $$\Q(\sqrt{21})$$ 25.2 25.2-b $$\bigl[0$$ , $$-a - 1$$ , $$a + 1$$ , $$a + 2$$ , $$-a - 2\bigr]$$
25.3-b1 $$\Q(\sqrt{21})$$ 25.3 25.3-b $$\bigl[0$$ , $$-a - 1$$ , $$a$$ , $$a + 2$$ , $$a + 1\bigr]$$
25.3-b2 $$\Q(\sqrt{21})$$ 25.3 25.3-b $$\bigl[0$$ , $$a + 1$$ , $$a$$ , $$a + 2$$ , $$0\bigr]$$
49.1-a1 $$\Q(\sqrt{21})$$ 49.1 49.1-a $$\bigl[0$$ , $$-a - 1$$ , $$1$$ , $$a + 2$$ , $$5 a - 16\bigr]$$
49.1-a2 $$\Q(\sqrt{21})$$ 49.1 49.1-a $$\bigl[0$$ , $$a + 1$$ , $$1$$ , $$a + 2$$ , $$-5 a - 9\bigr]$$
81.1-a3 $$\Q(\sqrt{21})$$ 81.1 81.1-a $$\bigl[0$$ , $$0$$ , $$1$$ , $$0$$ , $$3 a + 5\bigr]$$
81.1-a4 $$\Q(\sqrt{21})$$ 81.1 81.1-a $$\bigl[0$$ , $$0$$ , $$1$$ , $$0$$ , $$-3 a + 8\bigr]$$
81.1-b3 $$\Q(\sqrt{21})$$ 81.1 81.1-b $$\bigl[0$$ , $$0$$ , $$1$$ , $$0$$ , $$0\bigr]$$
81.1-b4 $$\Q(\sqrt{21})$$ 81.1 81.1-b $$\bigl[0$$ , $$0$$ , $$1$$ , $$0$$ , $$6 a - 17\bigr]$$
144.1-a1 $$\Q(\sqrt{21})$$ 144.1 144.1-a $$\bigl[0$$ , $$0$$ , $$0$$ , $$0$$ , $$-24 a - 43\bigr]$$
144.1-a2 $$\Q(\sqrt{21})$$ 144.1 144.1-a $$\bigl[0$$ , $$0$$ , $$0$$ , $$0$$ , $$1\bigr]$$
225.2-b1 $$\Q(\sqrt{21})$$ 225.2 225.2-b $$\bigl[0$$ , $$0$$ , $$a + 1$$ , $$0$$ , $$-4\bigr]$$
225.2-b2 $$\Q(\sqrt{21})$$ 225.2 225.2-b $$\bigl[0$$ , $$0$$ , $$a + 1$$ , $$0$$ , $$9 a + 16\bigr]$$
225.3-b1 $$\Q(\sqrt{21})$$ 225.3 225.3-b $$\bigl[0$$ , $$0$$ , $$a$$ , $$0$$ , $$-a - 3\bigr]$$
225.3-b2 $$\Q(\sqrt{21})$$ 225.3 225.3-b $$\bigl[0$$ , $$0$$ , $$a$$ , $$0$$ , $$-10 a + 26\bigr]$$
256.1-d1 $$\Q(\sqrt{21})$$ 256.1 256.1-d $$\bigl[0$$ , $$-a - 1$$ , $$0$$ , $$a + 2$$ , $$0\bigr]$$
256.1-d2 $$\Q(\sqrt{21})$$ 256.1 256.1-d $$\bigl[0$$ , $$a + 1$$ , $$0$$ , $$a + 2$$ , $$2\bigr]$$
400.2-a1 $$\Q(\sqrt{21})$$ 400.2 400.2-a $$\bigl[0$$ , $$a + 1$$ , $$0$$ , $$a + 2$$ , $$-8 a + 3\bigr]$$
400.2-a2 $$\Q(\sqrt{21})$$ 400.2 400.2-a $$\bigl[0$$ , $$-a - 1$$ , $$0$$ , $$a + 2$$ , $$416 a - 1163\bigr]$$
400.3-a1 $$\Q(\sqrt{21})$$ 400.3 400.3-a $$\bigl[0$$ , $$-a - 1$$ , $$0$$ , $$a + 2$$ , $$8 a - 7\bigr]$$
400.3-a2 $$\Q(\sqrt{21})$$ 400.3 400.3-a $$\bigl[0$$ , $$a + 1$$ , $$0$$ , $$a + 2$$ , $$-416 a - 745\bigr]$$
441.1-d1 $$\Q(\sqrt{21})$$ 441.1 441.1-d $$\bigl[0$$ , $$0$$ , $$1$$ , $$0$$ , $$-294 a - 527\bigr]$$
441.1-d2 $$\Q(\sqrt{21})$$ 441.1 441.1-d $$\bigl[0$$ , $$0$$ , $$1$$ , $$0$$ , $$12\bigr]$$
625.1-c1 $$\Q(\sqrt{21})$$ 625.1 625.1-c $$\bigl[0$$ , $$-a - 1$$ , $$1$$ , $$a + 2$$ , $$-a - 2\bigr]$$
625.1-c2 $$\Q(\sqrt{21})$$ 625.1 625.1-c $$\bigl[0$$ , $$a + 1$$ , $$1$$ , $$a + 2$$ , $$a - 1\bigr]$$
625.1-j1 $$\Q(\sqrt{21})$$ 625.1 625.1-j $$\bigl[0$$ , $$-a - 1$$ , $$a + 1$$ , $$a + 2$$ , $$-213 a + 588\bigr]$$
625.1-j2 $$\Q(\sqrt{21})$$ 625.1 625.1-j $$\bigl[0$$ , $$a + 1$$ , $$a + 1$$ , $$a + 2$$ , $$24 a + 34\bigr]$$
625.1-p1 $$\Q(\sqrt{21})$$ 625.1 625.1-p $$\bigl[0$$ , $$-a - 1$$ , $$1$$ , $$a + 2$$ , $$69 a - 192\bigr]$$
625.1-p2 $$\Q(\sqrt{21})$$ 625.1 625.1-p $$\bigl[0$$ , $$a + 1$$ , $$1$$ , $$a + 2$$ , $$-69 a - 121\bigr]$$
625.1-q1 $$\Q(\sqrt{21})$$ 625.1 625.1-q $$\bigl[0$$ , $$-a - 1$$ , $$a$$ , $$a + 2$$ , $$-25 a + 57\bigr]$$
625.1-q2 $$\Q(\sqrt{21})$$ 625.1 625.1-q $$\bigl[0$$ , $$a + 1$$ , $$a$$ , $$a + 2$$ , $$212 a + 378\bigr]$$
729.1-a1 $$\Q(\sqrt{21})$$ 729.1 729.1-a $$\bigl[0$$ , $$0$$ , $$a + 1$$ , $$0$$ , $$-15 a - 27\bigr]$$
729.1-a2 $$\Q(\sqrt{21})$$ 729.1 729.1-a $$\bigl[0$$ , $$0$$ , $$a + 1$$ , $$0$$ , $$-3\bigr]$$
729.1-b1 $$\Q(\sqrt{21})$$ 729.1 729.1-b $$\bigl[0$$ , $$0$$ , $$a$$ , $$0$$ , $$14 a - 41\bigr]$$
729.1-b2 $$\Q(\sqrt{21})$$ 729.1 729.1-b $$\bigl[0$$ , $$0$$ , $$a$$ , $$0$$ , $$-a - 2\bigr]$$
729.1-c1 $$\Q(\sqrt{21})$$ 729.1 729.1-c $$\bigl[0$$ , $$0$$ , $$a$$ , $$0$$ , $$-2\bigr]$$
729.1-c2 $$\Q(\sqrt{21})$$ 729.1 729.1-c $$\bigl[0$$ , $$0$$ , $$a$$ , $$0$$ , $$a + 1\bigr]$$
729.1-d1 $$\Q(\sqrt{21})$$ 729.1 729.1-d $$\bigl[0$$ , $$0$$ , $$a + 1$$ , $$0$$ , $$-a - 2\bigr]$$
729.1-d2 $$\Q(\sqrt{21})$$ 729.1 729.1-d $$\bigl[0$$ , $$0$$ , $$a + 1$$ , $$0$$ , $$-2 a + 2\bigr]$$
784.1-e1 $$\Q(\sqrt{21})$$ 784.1 784.1-e $$\bigl[0$$ , $$-a - 1$$ , $$0$$ , $$a + 2$$ , $$12 a + 21\bigr]$$
784.1-e2 $$\Q(\sqrt{21})$$ 784.1 784.1-e $$\bigl[0$$ , $$a + 1$$ , $$0$$ , $$a + 2$$ , $$-12 a + 35\bigr]$$
1225.2-a1 $$\Q(\sqrt{21})$$ 1225.2 1225.2-a $$\bigl[0$$ , $$a + 1$$ , $$a$$ , $$a + 2$$ , $$-182 a + 508\bigr]$$
1225.2-a2 $$\Q(\sqrt{21})$$ 1225.2 1225.2-a $$\bigl[0$$ , $$-a - 1$$ , $$a$$ , $$a + 2$$ , $$3 a - 3\bigr]$$
1225.2-b1 $$\Q(\sqrt{21})$$ 1225.2 1225.2-b $$\bigl[0$$ , $$-a - 1$$ , $$a$$ , $$a + 2$$ , $$17 a + 32\bigr]$$
1225.2-b2 $$\Q(\sqrt{21})$$ 1225.2 1225.2-b $$\bigl[0$$ , $$a + 1$$ , $$a$$ , $$a + 2$$ , $$56 a - 157\bigr]$$
1225.2-c1 $$\Q(\sqrt{21})$$ 1225.2 1225.2-c $$\bigl[0$$ , $$-a - 1$$ , $$1$$ , $$a + 2$$ , $$-18 a + 48\bigr]$$
1225.2-c2 $$\Q(\sqrt{21})$$ 1225.2 1225.2-c $$\bigl[0$$ , $$a + 1$$ , $$1$$ , $$a + 2$$ , $$-1\bigr]$$