# Properties

 Label 5040u Number of curves $4$ Conductor $5040$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5040.f1")

sage: E.isogeny_class()

## Elliptic curves in class 5040u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.f2 5040u1 [0, 0, 0, -1683, -26542] [2] 2304 $$\Gamma_0(N)$$-optimal
5040.f3 5040u2 [0, 0, 0, -1203, -41998] [2] 4608
5040.f1 5040u3 [0, 0, 0, -6723, 185922] [2] 6912
5040.f4 5040u4 [0, 0, 0, 10557, 984258] [2] 13824

## Rank

sage: E.rank()

The elliptic curves in class 5040u have rank $$0$$.

## Modular form5040.2.a.f

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} + 2q^{13} - 2q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.