# Properties

 Label 1344.q Number of curves $6$ Conductor $1344$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 1344.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1344.q1 1344g4 [0, 1, 0, -86017, 9681503] [2] 3072
1344.q2 1344g5 [0, 1, 0, -58497, -5412897] [2] 6144
1344.q3 1344g3 [0, 1, 0, -6657, 71775] [2, 2] 3072
1344.q4 1344g2 [0, 1, 0, -5377, 149855] [2, 2] 1536
1344.q5 1344g1 [0, 1, 0, -257, 3423] [2] 768 $$\Gamma_0(N)$$-optimal
1344.q6 1344g6 [0, 1, 0, 24703, 579807] [4] 6144

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 1344.q do not have complex multiplication.

## Modular form1344.2.a.q

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.