# Properties

 Label 13552c Number of curves $4$ Conductor $13552$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("c1")

sage: E.isogeny_class()

## Elliptic curves in class 13552c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
13552.p4 13552c1 [0, 0, 0, 121, 2662]  5120 $$\Gamma_0(N)$$-optimal
13552.p3 13552c2 [0, 0, 0, -2299, 39930] [2, 2] 10240
13552.p2 13552c3 [0, 0, 0, -7139, -183678]  20480
13552.p1 13552c4 [0, 0, 0, -36179, 2648690]  20480

## Rank

sage: E.rank()

The elliptic curves in class 13552c have rank $$0$$.

## Complex multiplication

The elliptic curves in class 13552c do not have complex multiplication.

## Modular form 13552.2.a.c

sage: E.q_eigenform(10)

$$q + 2q^{5} - q^{7} - 3q^{9} - 2q^{13} + 6q^{17} + 8q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 