# Properties

 Label 250173bh Number of curves 4 Conductor 250173 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("250173.bh1")

sage: E.isogeny_class()

## Elliptic curves in class 250173bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
250173.bh3 250173bh1 [1, -1, 0, -340379928, -2417011415861] [2] 29675520 $$\Gamma_0(N)$$-optimal
250173.bh2 250173bh2 [1, -1, 0, -341175933, -2405138046080] [2, 2] 59351040
250173.bh1 250173bh3 [1, -1, 0, -602606718, 1786486302139] [2] 118702080
250173.bh4 250173bh4 [1, -1, 0, -92481228, -5836876280375] [2] 118702080

## Rank

sage: E.rank()

The elliptic curves in class 250173bh have rank $$0$$.

## Modular form 250173.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{2} - q^{4} - 2q^{5} + q^{7} - 3q^{8} - 2q^{10} - q^{11} - 2q^{13} + q^{14} - q^{16} + 2q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.