# Properties

 Label 25200eh Number of curves 6 Conductor 25200 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.eu1")

sage: E.isogeny_class()

## Elliptic curves in class 25200eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.eu5 25200eh1 [0, 0, 0, -1875, 63250] [2] 27648 $$\Gamma_0(N)$$-optimal
25200.eu4 25200eh2 [0, 0, 0, -37875, 2835250] [2] 55296
25200.eu6 25200eh3 [0, 0, 0, 16125, -1322750] [2] 82944
25200.eu3 25200eh4 [0, 0, 0, -127875, -14426750] [2] 165888
25200.eu2 25200eh5 [0, 0, 0, -613875, -185660750] [2] 248832
25200.eu1 25200eh6 [0, 0, 0, -9829875, -11862332750] [2] 497664

## Rank

sage: E.rank()

The elliptic curves in class 25200eh have rank $$0$$.

## Modular form 25200.2.a.eu

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.