# Properties

 Label 371280fv Number of curves 4 Conductor 371280 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("371280.fv1")

sage: E.isogeny_class()

## Elliptic curves in class 371280fv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
371280.fv4 371280fv1 [0, 1, 0, -86840, 32340] [2] 2654208 $$\Gamma_0(N)$$-optimal
371280.fv2 371280fv2 [0, 1, 0, -952120, -356809132] [2, 2] 5308416
371280.fv3 371280fv3 [0, 1, 0, -527800, -676067500] [2] 10616832
371280.fv1 371280fv4 [0, 1, 0, -15220920, -22861560492] [2] 10616832

## Rank

sage: E.rank()

The elliptic curves in class 371280fv have rank $$0$$.

## Modular form 371280.2.a.fv

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} - q^{7} + q^{9} + 4q^{11} + q^{13} + q^{15} + q^{17} + 4q^{19} + O(q^{20})$$

## 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 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.