# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 13552.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
13552.p1 13552c4 $$[0, 0, 0, -36179, 2648690]$$ $$1443468546/7$$ $$25397098496$$ $$$$ $$20480$$ $$1.1969$$
13552.p2 13552c3 $$[0, 0, 0, -7139, -183678]$$ $$11090466/2401$$ $$8711204784128$$ $$$$ $$20480$$ $$1.1969$$
13552.p3 13552c2 $$[0, 0, 0, -2299, 39930]$$ $$740772/49$$ $$88889844736$$ $$[2, 2]$$ $$10240$$ $$0.85034$$
13552.p4 13552c1 $$[0, 0, 0, 121, 2662]$$ $$432/7$$ $$-3174637312$$ $$$$ $$5120$$ $$0.50377$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 13552.2.a.p

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 