# Properties

 Label 2520.f Number of curves $6$ Conductor $2520$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2520.f1")

sage: E.isogeny_class()

## Elliptic curves in class 2520.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2520.f1 2520e5 [0, 0, 0, -94323, 11149742] [2] 8192
2520.f2 2520e3 [0, 0, 0, -6123, 160022] [2, 2] 4096
2520.f3 2520e2 [0, 0, 0, -1623, -22678] [2, 2] 2048
2520.f4 2520e1 [0, 0, 0, -1578, -24127] [2] 1024 $$\Gamma_0(N)$$-optimal
2520.f5 2520e4 [0, 0, 0, 2157, -112642] [2] 4096
2520.f6 2520e6 [0, 0, 0, 10077, 863102] [2] 8192

## Rank

sage: E.rank()

The elliptic curves in class 2520.f have rank $$0$$.

## Modular form2520.2.a.f

sage: E.q_eigenform(10)

$$q - q^{5} - q^{7} + 4q^{11} - 2q^{13} - 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.