# Properties

 Label 5040.d Number of curves 4 Conductor 5040 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5040.d1")

sage: E.isogeny_class()

## Elliptic curves in class 5040.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.d1 5040bd3 [0, 0, 0, -16203, -793798] [2] 8192
5040.d2 5040bd2 [0, 0, 0, -1083, -10582] [2, 2] 4096
5040.d3 5040bd1 [0, 0, 0, -363, 2522] [2] 2048 $$\Gamma_0(N)$$-optimal
5040.d4 5040bd4 [0, 0, 0, 2517, -66022] [2] 8192

## Rank

sage: E.rank()

The elliptic curves in class 5040.d have rank $$1$$.

## Modular form5040.2.a.d

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} - 6q^{13} - 2q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.