# Properties

 Label 19600.bu Number of curves $4$ Conductor $19600$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.bu1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.bu

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bu1 19600cc3 [0, 0, 0, -5246675, -4625440750] [2] 442368
19600.bu2 19600cc4 [0, 0, 0, -1718675, 810423250] [2] 442368
19600.bu3 19600cc2 [0, 0, 0, -346675, -63540750] [2, 2] 221184
19600.bu4 19600cc1 [0, 0, 0, 45325, -5916750] [2] 110592 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 19600.bu have rank $$1$$.

## Modular form 19600.2.a.bu

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.