# Properties

 Label 1344r Number of curves 6 Conductor 1344 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1344.s1")

sage: E.isogeny_class()

## Elliptic curves in class 1344r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1344.s6 1344r1 [0, 1, 0, 63, 63] [2] 256 $$\Gamma_0(N)$$-optimal
1344.s5 1344r2 [0, 1, 0, -257, 255] [2, 2] 512
1344.s3 1344r3 [0, 1, 0, -2497, -48577] [2] 1024
1344.s2 1344r4 [0, 1, 0, -3137, 66495] [2, 2] 1024
1344.s1 1344r5 [0, 1, 0, -50177, 4309503] [2] 2048
1344.s4 1344r6 [0, 1, 0, -2177, 108927] [2] 2048

## Rank

sage: E.rank()

The elliptic curves in class 1344r have rank $$0$$.

## Modular form1344.2.a.s

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{5} + q^{7} + q^{9} + 4q^{11} + 2q^{13} + 2q^{15} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.