# Properties

 Label 145794.r Number of curves 4 Conductor 145794 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("145794.r1")

sage: E.isogeny_class()

## Elliptic curves in class 145794.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
145794.r1 145794w3 [1, 0, 1, -177871, 28748354]  1251936
145794.r2 145794w4 [1, 0, 1, -89511, 57341650]  2503872
145794.r3 145794w1 [1, 0, 1, -12196, -489970]  417312 $$\Gamma_0(N)$$-optimal
145794.r4 145794w2 [1, 0, 1, 9894, -2062778]  834624

## Rank

sage: E.rank()

The elliptic curves in class 145794.r have rank $$0$$.

## Modular form 145794.2.a.r

sage: E.q_eigenform(10)

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

## 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. 