# Properties

 Label 232050fv Number of curves 4 Conductor 232050 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("232050.fv1")

sage: E.isogeny_class()

## Elliptic curves in class 232050fv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
232050.fv4 232050fv1 [1, 0, 0, -135688, -131008]  2654208 $$\Gamma_0(N)$$-optimal
232050.fv2 232050fv2 [1, 0, 0, -1487688, 696148992] [2, 2] 5308416
232050.fv1 232050fv3 [1, 0, 0, -23782688, 44639593992]  10616832
232050.fv3 232050fv4 [1, 0, 0, -824688, 1320031992]  10616832

## Rank

sage: E.rank()

The elliptic curves in class 232050fv have rank $$1$$.

## Modular form 232050.2.a.fv

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} - q^{7} + q^{8} + q^{9} - 4q^{11} + q^{12} - q^{13} - q^{14} + q^{16} - q^{17} + q^{18} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 