# Properties

 Label 19600.g Number of curves 2 Conductor 19600 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.g1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.g1 19600db1 [0, 0, 0, -52675, 4653250] [] 69120 $$\Gamma_0(N)$$-optimal
19600.g2 19600db2 [0, 0, 0, 367325, -44150750] [] 483840

## Rank

sage: E.rank()

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

## Modular form 19600.2.a.g

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 