# Properties

 Label 61347.s Number of curves 2 Conductor 61347 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61347.s1")

sage: E.isogeny_class()

## Elliptic curves in class 61347.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.s1 61347w1 [0, 1, 1, -12393, -540952] [] 80640 $$\Gamma_0(N)$$-optimal
61347.s2 61347w2 [0, 1, 1, 43377, -2721559] [] 241920

## Rank

sage: E.rank()

The elliptic curves in class 61347.s have rank $$1$$.

## Modular form 61347.2.a.s

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{4} - q^{7} + q^{9} - 2q^{12} + 4q^{16} - 6q^{17} - q^{19} + O(q^{20})$$

## 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 LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 