# Properties

 Label 71148v Number of curves 2 Conductor 71148 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("71148.l1")

sage: E.isogeny_class()

## Elliptic curves in class 71148v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
71148.l2 71148v1 [0, -1, 0, 15811, -427986] [2] 259200 $$\Gamma_0(N)$$-optimal
71148.l1 71148v2 [0, -1, 0, -73124, -3594072] [2] 518400

## Rank

sage: E.rank()

The elliptic curves in class 71148v have rank $$0$$.

## Modular form 71148.2.a.l

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + q^{9} - 2q^{13} + 2q^{15} + 4q^{17} - 6q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.