# Properties

 Label 61200fh Number of curves 6 Conductor 61200 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("61200.do1")

sage: E.isogeny_class()

## Elliptic curves in class 61200fh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
61200.do5 61200fh1 [0, 0, 0, -122475, 15300250] [2] 393216 $$\Gamma_0(N)$$-optimal
61200.do4 61200fh2 [0, 0, 0, -410475, -83483750] [2, 2] 786432
61200.do6 61200fh3 [0, 0, 0, 813525, -486179750] [2] 1572864
61200.do2 61200fh4 [0, 0, 0, -6242475, -6002963750] [2, 2] 1572864
61200.do3 61200fh5 [0, 0, 0, -5918475, -6653879750] [2] 3145728
61200.do1 61200fh6 [0, 0, 0, -99878475, -384198767750] [2] 3145728

## Rank

sage: E.rank()

The elliptic curves in class 61200fh have rank $$0$$.

## Modular form 61200.2.a.do

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.