# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("371280.fk1")

sage: E.isogeny_class()

## Elliptic curves in class 371280fk

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
371280.fk4 371280fk1 [0, 1, 0, -5320, 10289780] [2] 2949120 $$\Gamma_0(N)$$-optimal
371280.fk3 371280fk2 [0, 1, 0, -742600, 242975348] [2, 2] 5898240
371280.fk1 371280fk3 [0, 1, 0, -11840200, 15677517428] [2] 11796480
371280.fk2 371280fk4 [0, 1, 0, -1441480, -287893900] [2] 11796480

## Rank

sage: E.rank()

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

## Modular form 371280.2.a.fk

sage: E.q_eigenform(10)

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

## 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.