# Properties

 Label 1344.o Number of curves $4$ Conductor $1344$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1344.o1")

sage: E.isogeny_class()

## Elliptic curves in class 1344.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1344.o1 1344p4 [0, 1, 0, -7313, 238287]  1152
1344.o2 1344p3 [0, 1, 0, -453, 3675]  576
1344.o3 1344p2 [0, 1, 0, -113, 111]  384
1344.o4 1344p1 [0, 1, 0, 27, 27]  192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1344.o have rank $$1$$.

## Modular form1344.2.a.o

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - 6q^{11} - 2q^{13} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 