# Properties

 Label 61200.w Number of curves 4 Conductor 61200 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61200.w1")

sage: E.isogeny_class()

## Elliptic curves in class 61200.w

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61200.w1 61200fd4 [0, 0, 0, -406875, -69029750]  995328
61200.w2 61200fd3 [0, 0, 0, -370875, -86921750]  497664
61200.w3 61200fd2 [0, 0, 0, -154875, 23454250]  331776
61200.w4 61200fd1 [0, 0, 0, -10875, 270250]  165888 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 61200.w have rank $$1$$.

## Modular form 61200.2.a.w

sage: E.q_eigenform(10)

$$q - 4q^{7} + 6q^{11} - 2q^{13} - q^{17} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 