# Properties

 Label 2070.b Number of curves $6$ Conductor $2070$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2070.b1")

sage: E.isogeny_class()

## Elliptic curves in class 2070.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2070.b1 2070f3 [1, -1, 0, -993600, -380962764] [2] 12288
2070.b2 2070f5 [1, -1, 0, -232470, 37012950] [2] 24576
2070.b3 2070f4 [1, -1, 0, -63720, -5613300] [2, 2] 12288
2070.b4 2070f2 [1, -1, 0, -62100, -5940864] [2, 2] 6144
2070.b5 2070f1 [1, -1, 0, -3780, -97200] [2] 3072 $$\Gamma_0(N)$$-optimal
2070.b6 2070f6 [1, -1, 0, 79110, -27294894] [2] 24576

## Rank

sage: E.rank()

The elliptic curves in class 2070.b have rank $$1$$.

## Modular form2070.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} - 2q^{13} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.