# Properties

 Label 19600.bv Number of curves 4 Conductor 19600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("19600.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 19600.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19600.bv1 19600i3 [0, 0, 0, -131075, -18264750] [2] 55296
19600.bv2 19600i2 [0, 0, 0, -8575, -257250] [2, 2] 27648
19600.bv3 19600i1 [0, 0, 0, -2450, 42875] [2] 13824 $$\Gamma_0(N)$$-optimal
19600.bv4 19600i4 [0, 0, 0, 15925, -1457750] [2] 55296

## Rank

sage: E.rank()

The elliptic curves in class 19600.bv have rank $$0$$.

## Modular form 19600.2.a.bv

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.