# Properties

 Label 346560.kp Number of curves $2$ Conductor $346560$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("346560.kp1")

sage: E.isogeny_class()

## Elliptic curves in class 346560.kp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.kp1 346560kp2 [0, 1, 0, -1649985, -816213825] [2] 3932160
346560.kp2 346560kp1 [0, 1, 0, -93505, -15249217] [2] 1966080 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 346560.kp have rank $$0$$.

## Modular form 346560.2.a.kp

sage: E.q_eigenform(10)

$$q + q^{3} + q^{5} + 2q^{7} + q^{9} + 2q^{13} + q^{15} - 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.