# Properties

 Label 1344.i Number of curves $6$ Conductor $1344$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1344.i1")

sage: E.isogeny_class()

## Elliptic curves in class 1344.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1344.i1 1344m3 [0, -1, 0, -86017, -9681503] [2] 3072
1344.i2 1344m5 [0, -1, 0, -58497, 5412897] [4] 6144
1344.i3 1344m4 [0, -1, 0, -6657, -71775] [2, 2] 3072
1344.i4 1344m2 [0, -1, 0, -5377, -149855] [2, 2] 1536
1344.i5 1344m1 [0, -1, 0, -257, -3423] [2] 768 $$\Gamma_0(N)$$-optimal
1344.i6 1344m6 [0, -1, 0, 24703, -579807] [2] 6144

## Rank

sage: E.rank()

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

## Modular form1344.2.a.i

sage: E.q_eigenform(10)

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

## 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.