# Properties

 Label 158.d Number of curves $2$ Conductor $158$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 158.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
158.d1 158c2 [1, 1, 1, -23380, -1385691] [] 240
158.d2 158c1 [1, 1, 1, -420, 3109]  48 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 158.d have rank $$0$$.

## Complex multiplication

The elliptic curves in class 158.d do not have complex multiplication.

## Modular form158.2.a.d

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} + q^{8} - 2q^{9} + q^{10} + 2q^{11} - q^{12} - q^{13} + 3q^{14} - q^{15} + q^{16} - 2q^{17} - 2q^{18} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 