# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("61347.t1")

sage: E.isogeny_class()

## Elliptic curves in class 61347v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61347.t1 61347v1 [0, 1, 1, -1499593, 714008455] [] 887040 $$\Gamma_0(N)$$-optimal
61347.t2 61347v2 [0, 1, 1, 5248577, 3643389052] [] 2661120

## Rank

sage: E.rank()

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

## Modular form 61347.2.a.t

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 Cremona 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 Cremona labels. 