# Properties

 Label 182070bb Number of curves $4$ Conductor $182070$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 182070bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.cp3 182070bb1 [1, -1, 1, -9158, 215237]  589824 $$\Gamma_0(N)$$-optimal
182070.cp2 182070bb2 [1, -1, 1, -61178, -5652619] [2, 2] 1179648
182070.cp4 182070bb3 [1, -1, 1, 16852, -19136203]  2359296
182070.cp1 182070bb4 [1, -1, 1, -971528, -368336059]  2359296

## Rank

sage: E.rank()

The elliptic curves in class 182070bb have rank $$0$$.

## Complex multiplication

The elliptic curves in class 182070bb do not have complex multiplication.

## Modular form 182070.2.a.bb

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + q^{7} + q^{8} - q^{10} - 4q^{11} - 2q^{13} + q^{14} + q^{16} + O(q^{20})$$

## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 