# Properties

 Label 61347i Number of curves 2 Conductor 61347 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61347.v1")

sage: E.isogeny_class()

## Elliptic curves in class 61347i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.v2 61347i1 [1, 1, 0, -1212, -16947] [] 33600 $$\Gamma_0(N)$$-optimal
61347.v1 61347i2 [1, 1, 0, -9077, 1847058] [] 235200

## Rank

sage: E.rank()

The elliptic curves in class 61347i have rank $$0$$.

## Modular form 61347.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} + 2q^{7} - 3q^{8} + q^{9} + q^{10} + q^{12} + 2q^{14} - q^{15} - q^{16} + 7q^{17} + q^{18} - 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 