# Properties

 Label 5610.m Number of curves $2$ Conductor $5610$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5610.m1")

sage: E.isogeny_class()

## Elliptic curves in class 5610.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.m1 5610k1 [1, 0, 1, -8504, 301106]  8064 $$\Gamma_0(N)$$-optimal
5610.m2 5610k2 [1, 0, 1, -8254, 319706]  16128

## Rank

sage: E.rank()

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

## Modular form5610.2.a.m

sage: E.q_eigenform(10)

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

## 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. 