# Properties

 Label 67158r Number of curves 2 Conductor 67158 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("67158.q1")

sage: E.isogeny_class()

## Elliptic curves in class 67158r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67158.q1 67158r1 [1, -1, 0, -1402254, -638940204] [] 1053696 $$\Gamma_0(N)$$-optimal
67158.q2 67158r2 [1, -1, 0, 7781256, 28217419146] [] 7375872

## Rank

sage: E.rank()

The elliptic curves in class 67158r have rank $$0$$.

## Modular form 67158.2.a.q

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2q^{11} - q^{13} - q^{14} + q^{16} - 4q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 