# Properties

 Label 145.a Number of curves 2 Conductor 145 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("145.a1")

sage: E.isogeny_class()

## Elliptic curves in class 145.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
145.a1 145a1 [1, -1, 1, -3, 2]  4 $$\Gamma_0(N)$$-optimal
145.a2 145a2 [1, -1, 1, 2, 6]  8

## Rank

sage: E.rank()

The elliptic curves in class 145.a have rank $$1$$.

## Modular form145.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - q^{5} - 2q^{7} + 3q^{8} - 3q^{9} + q^{10} - 6q^{11} + 2q^{13} + 2q^{14} - q^{16} - 2q^{17} + 3q^{18} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 