# Properties

 Label 193600.v Number of curves 2 Conductor 193600 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("193600.v1")

sage: E.isogeny_class()

## Elliptic curves in class 193600.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
193600.v1 193600i2 [0, 1, 0, -4456833, -4195121537] [] 12441600
193600.v2 193600i1 [0, 1, 0, 383167, 30198463] [] 4147200 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 193600.v have rank $$0$$.

## Modular form 193600.2.a.v

sage: E.q_eigenform(10)

$$q - 2q^{3} - 4q^{7} + q^{9} + 5q^{13} + 7q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.