# Properties

 Label 5520.i Number of curves $6$ Conductor $5520$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("5520.i1")

sage: E.isogeny_class()

## Elliptic curves in class 5520.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5520.i1 5520u3 [0, -1, 0, -1766400, -903022848] [2] 36864
5520.i2 5520u5 [0, -1, 0, -413280, 87734400] [4] 73728
5520.i3 5520u4 [0, -1, 0, -113280, -13305600] [2, 4] 36864
5520.i4 5520u2 [0, -1, 0, -110400, -14082048] [2, 2] 18432
5520.i5 5520u1 [0, -1, 0, -6720, -230400] [2] 9216 $$\Gamma_0(N)$$-optimal
5520.i6 5520u6 [0, -1, 0, 140640, -64699008] [4] 73728

## Rank

sage: E.rank()

The elliptic curves in class 5520.i have rank $$0$$.

## Modular form5520.2.a.i

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.