# Properties

 Label 25200.eh Number of curves 8 Conductor 25200 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.eh1")

sage: E.isogeny_class()

## Elliptic curves in class 25200.eh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.eh1 25200eg8 [0, 0, 0, -1264437075, -17305890272750] [2] 5308416
25200.eh2 25200eg6 [0, 0, 0, -79029075, -270391904750] [2, 2] 2654208
25200.eh3 25200eg7 [0, 0, 0, -73269075, -311477984750] [2] 5308416
25200.eh4 25200eg5 [0, 0, 0, -15687075, -23494022750] [2] 1769472
25200.eh5 25200eg3 [0, 0, 0, -5301075, -3570272750] [2] 1327104
25200.eh6 25200eg2 [0, 0, 0, -2079075, 605745250] [2, 2] 884736
25200.eh7 25200eg1 [0, 0, 0, -1791075, 922257250] [2] 442368 $$\Gamma_0(N)$$-optimal
25200.eh8 25200eg4 [0, 0, 0, 6920925, 4448745250] [2] 1769472

## Rank

sage: E.rank()

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

## Modular form 25200.2.a.eh

sage: E.q_eigenform(10)

$$q + q^{7} - 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.