# Properties

 Label 19350.cv Number of curves $2$ Conductor $19350$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cv1")

sage: E.isogeny_class()

## Elliptic curves in class 19350.cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19350.cv1 19350cj2 [1, -1, 1, -37299605, 87689980397] [2] 1935360
19350.cv2 19350cj1 [1, -1, 1, -2307605, 1399708397] [2] 967680 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 19350.cv have rank $$0$$.

## Complex multiplication

The elliptic curves in class 19350.cv do not have complex multiplication.

## Modular form 19350.2.a.cv

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 4q^{7} + q^{8} + 4q^{11} - 4q^{13} + 4q^{14} + q^{16} + 4q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.