# Properties

 Label 43120cv Number of curves 4 Conductor 43120 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("43120.q1")

sage: E.isogeny_class()

## Elliptic curves in class 43120cv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43120.q3 43120cv1 [0, 1, 0, -43920, 68929300] [2] 663552 $$\Gamma_0(N)$$-optimal
43120.q2 43120cv2 [0, 1, 0, -2803600, 1789865748] [2] 1327104
43120.q4 43120cv3 [0, 1, 0, 395120, -1857051372] [2] 1990656
43120.q1 43120cv4 [0, 1, 0, -20474960, -34656469100] [2] 3981312

## Rank

sage: E.rank()

The elliptic curves in class 43120cv have rank $$1$$.

## Modular form 43120.2.a.q

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{5} + q^{9} + q^{11} + 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.