# Properties

 Label 118354.b Number of curves $4$ Conductor $118354$ CM no Rank $2$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 118354.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
118354.b1 118354e4 [1, 0, 1, -393426, 65602682]  2505600
118354.b2 118354e3 [1, 0, 1, -358616, 82617810]  1252800
118354.b3 118354e2 [1, 0, 1, -149756, -22313454]  835200
118354.b4 118354e1 [1, 0, 1, -10516, -257838]  417600 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 118354.b have rank $$2$$.

## Complex multiplication

The elliptic curves in class 118354.b do not have complex multiplication.

## Modular form 118354.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} - 2q^{3} + q^{4} + 2q^{6} - 4q^{7} - q^{8} + q^{9} - 6q^{11} - 2q^{12} - 2q^{13} + 4q^{14} + q^{16} - q^{17} - q^{18} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 