# Properties

 Label 6272.b Number of curves $2$ Conductor $6272$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6272.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6272.b1 6272g2 [0, 1, 0, -457, 3303]  2304
6272.b2 6272g1 [0, 1, 0, 33, 265]  1152 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6272.b have rank $$1$$.

## Complex multiplication

The elliptic curves in class 6272.b do not have complex multiplication.

## Modular form6272.2.a.b

sage: E.q_eigenform(10)

$$q - 2q^{3} + 2q^{5} + q^{9} - 2q^{11} + 2q^{13} - 4q^{15} + 2q^{17} - 2q^{19} + O(q^{20})$$

## 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 LMFDB 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 LMFDB labels. 