# Properties

 Label 12144bb Number of curves 2 Conductor 12144 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("12144.bh1")

sage: E.isogeny_class()

## Elliptic curves in class 12144bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12144.bh2 12144bb1 [0, 1, 0, -368, 39444] [2] 10240 $$\Gamma_0(N)$$-optimal
12144.bh1 12144bb2 [0, 1, 0, -19808, 1058100] [2] 20480

## Rank

sage: E.rank()

The elliptic curves in class 12144bb have rank $$1$$.

## Modular form 12144.2.a.bh

sage: E.q_eigenform(10)

$$q + q^{3} + 2q^{7} + q^{9} - q^{11} + 2q^{13} - 2q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.