# Properties

 Label 15600.n Number of curves $6$ Conductor $15600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("15600.n1")

sage: E.isogeny_class()

## Elliptic curves in class 15600.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
15600.n1 15600z5 [0, -1, 0, -3606008, 2636854512] [2] 294912
15600.n2 15600z3 [0, -1, 0, -338008, -75465488] [2] 147456
15600.n3 15600z4 [0, -1, 0, -226008, 41014512] [2, 2] 147456
15600.n4 15600z6 [0, -1, 0, -46008, 104374512] [2] 294912
15600.n5 15600z2 [0, -1, 0, -26008, -585488] [2, 2] 73728
15600.n6 15600z1 [0, -1, 0, 5992, -73488] [2] 36864 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 15600.n have rank $$0$$.

## Modular form 15600.2.a.n

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.