# Properties

 Label 5610.g Number of curves $4$ Conductor $5610$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("5610.g1")

sage: E.isogeny_class()

## Elliptic curves in class 5610.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5610.g1 5610f3 [1, 1, 0, -567947, 164507661] [2] 36864
5610.g2 5610f2 [1, 1, 0, -35547, 2551581] [2, 2] 18432
5610.g3 5610f4 [1, 1, 0, -15147, 5485101] [2] 36864
5610.g4 5610f1 [1, 1, 0, -3547, -14819] [2] 9216 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5610.g have rank $$0$$.

## Modular form5610.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.