# Properties

 Label 92a Number of curves 2 Conductor 92 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("92.b1")

sage: E.isogeny_class()

## Elliptic curves in class 92a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92.b2 92a1 [0, 1, 0, 2, 1]  2 $$\Gamma_0(N)$$-optimal
92.b1 92a2 [0, 1, 0, -18, -43] [] 6

## Rank

sage: E.rank()

The elliptic curves in class 92a have rank $$0$$.

## Modular form92.2.a.b

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} - 2q^{9} - q^{13} - 6q^{17} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 