# Properties

 Label 346560.ik Number of curves $4$ Conductor $346560$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("346560.ik1")

sage: E.isogeny_class()

## Elliptic curves in class 346560.ik

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
346560.ik1 346560ik4 [0, 1, 0, -70236641, -226588880001] [2] 26542080
346560.ik2 346560ik3 [0, 1, 0, -5083361, -2348756865] [2] 26542080
346560.ik3 346560ik2 [0, 1, 0, -4390241, -3540784641] [2, 2] 13271040
346560.ik4 346560ik1 [0, 1, 0, -231521, -73243905] [2] 6635520 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 346560.ik have rank $$1$$.

## Modular form 346560.2.a.ik

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + 4q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.