# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.fq1")

sage: E.isogeny_class()

## Elliptic curves in class 25200er

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.fq6 25200er1 [0, 0, 0, 35925, -3667750] [2] 147456 $$\Gamma_0(N)$$-optimal
25200.fq5 25200er2 [0, 0, 0, -252075, -37939750] [2, 2] 294912
25200.fq4 25200er3 [0, 0, 0, -1332075, 559300250] [4] 589824
25200.fq2 25200er4 [0, 0, 0, -3780075, -2828587750] [2, 2] 589824
25200.fq3 25200er5 [0, 0, 0, -3528075, -3221959750] [2] 1179648
25200.fq1 25200er6 [0, 0, 0, -60480075, -181036687750] [2] 1179648

## Rank

sage: E.rank()

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

## Modular form 25200.2.a.fq

sage: E.q_eigenform(10)

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

## 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 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.