# Properties

 Label 481650hr Number of curves $4$ Conductor $481650$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("481650.hr1")

sage: E.isogeny_class()

## Elliptic curves in class 481650hr

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
481650.hr3 481650hr1 [1, 0, 0, -131063, 18142617]  3538944 $$\Gamma_0(N)$$-optimal
481650.hr2 481650hr2 [1, 0, 0, -215563, -8136883] [2, 2] 7077888
481650.hr4 481650hr3 [1, 0, 0, 840687, -64118133]  14155776
481650.hr1 481650hr4 [1, 0, 0, -2623813, -1633705633]  14155776

## Rank

sage: E.rank()

The elliptic curves in class 481650hr have rank $$0$$.

## Modular form 481650.2.a.hr

sage: E.q_eigenform(10)

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

## 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 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. 