# Properties

 Label 58870.d Number of curves $4$ Conductor $58870$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("58870.d1")

sage: E.isogeny_class()

## Elliptic curves in class 58870.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
58870.d1 58870a4 [1, -1, 0, -225125, -41055189]  387072
58870.d2 58870a3 [1, -1, 0, -73745, 7221575]  387072
58870.d3 58870a2 [1, -1, 0, -14875, -561039] [2, 2] 193536
58870.d4 58870a1 [1, -1, 0, 1945, -53075]  96768 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 58870.d have rank $$1$$.

## Modular form 58870.2.a.d

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{7} - q^{8} - 3q^{9} + q^{10} - 4q^{11} - 6q^{13} + q^{14} + q^{16} - 2q^{17} + 3q^{18} + O(q^{20})$$

## 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. 