# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("61347.f1")

sage: E.isogeny_class()

## Elliptic curves in class 61347m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.f2 61347m1 [1, 1, 1, -204916, -36208138] [] 436800 $$\Gamma_0(N)$$-optimal
61347.f1 61347m2 [1, 1, 1, -1534101, 4065656772] [] 3057600

## Rank

sage: E.rank()

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

## Modular form 61347.2.a.f

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. 