# Properties

 Label 152592d Number of curves 2 Conductor 152592 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("152592.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 152592d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
152592.bv2 152592d1 [0, 1, 0, 771, 4806]  118272 $$\Gamma_0(N)$$-optimal
152592.bv1 152592d2 [0, 1, 0, -3564, 37752]  236544

## Rank

sage: E.rank()

The elliptic curves in class 152592d have rank $$0$$.

## Modular form 152592.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{3} - 2q^{5} - 2q^{7} + q^{9} + q^{11} - 2q^{13} - 2q^{15} + 6q^{19} + O(q^{20})$$

## 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. 