# Properties

 Label 61347.u Number of curves 4 Conductor 61347 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61347.u1")

sage: E.isogeny_class()

## Elliptic curves in class 61347.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.u1 61347k4 [1, 1, 0, -1421631, 651813804]  860160
61347.u2 61347k3 [1, 1, 0, -399181, -88071914]  860160
61347.u3 61347k2 [1, 1, 0, -92446, 9285775] [2, 2] 430080
61347.u4 61347k1 [1, 1, 0, 9799, 799440]  215040 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 61347.2.a.u

sage: E.q_eigenform(10)

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

## 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. 