# Properties

 Label 5610.o Number of curves $4$ Conductor $5610$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.o1")

sage: E.isogeny_class()

## Elliptic curves in class 5610.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.o1 5610n4 [1, 0, 1, -220364, -39529438]  69120
5610.o2 5610n3 [1, 0, 1, -23844, 403426]  34560
5610.o3 5610n2 [1, 0, 1, -18899, 966116]  23040
5610.o4 5610n1 [1, 0, 1, -18729, 984952]  11520 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5610.o have rank $$1$$.

## Modular form5610.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + 2q^{7} - q^{8} + q^{9} + q^{10} + q^{11} + q^{12} - 4q^{13} - 2q^{14} - q^{15} + q^{16} - q^{17} - q^{18} + 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 