# Properties

 Label 67600.cb Number of curves 4 Conductor 67600 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("67600.cb1")

sage: E.isogeny_class()

## Elliptic curves in class 67600.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
67600.cb1 67600b4 [0, 0, 0, -452075, 116990250] [2] 442368
67600.cb2 67600b2 [0, 0, 0, -29575, 1647750] [2, 2] 221184
67600.cb3 67600b1 [0, 0, 0, -8450, -274625] [2] 110592 $$\Gamma_0(N)$$-optimal
67600.cb4 67600b3 [0, 0, 0, 54925, 9337250] [2] 442368

## Rank

sage: E.rank()

The elliptic curves in class 67600.cb have rank $$1$$.

## Modular form 67600.2.a.cb

sage: E.q_eigenform(10)

$$q + 4q^{7} - 3q^{9} + 4q^{11} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.