# Properties

 Label 10608.p Number of curves $6$ Conductor $10608$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("10608.p1")

sage: E.isogeny_class()

## Elliptic curves in class 10608.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
10608.p1 10608ba5 [0, 1, 0, -322784, 70467252] [4] 65536
10608.p2 10608ba3 [0, 1, 0, -22224, 857556] [2, 4] 32768
10608.p3 10608ba2 [0, 1, 0, -8704, -305164] [2, 2] 16384
10608.p4 10608ba1 [0, 1, 0, -8624, -311148] [2] 8192 $$\Gamma_0(N)$$-optimal
10608.p5 10608ba4 [0, 1, 0, 3536, -1083628] [2] 32768
10608.p6 10608ba6 [0, 1, 0, 62016, 5878260] [4] 65536

## Rank

sage: E.rank()

The elliptic curves in class 10608.p have rank $$1$$.

## Modular form 10608.2.a.p

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.