# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("61347.g1")

sage: E.isogeny_class()

## Elliptic curves in class 61347l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.g2 61347l1 [1, 1, 1, 40472, -3939616]  322560 $$\Gamma_0(N)$$-optimal
61347.g1 61347l2 [1, 1, 1, -266263, -39888958]  645120

## Rank

sage: E.rank()

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

## Modular form 61347.2.a.g

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 