# Properties

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

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("25200.q1")

sage: E.isogeny_class()

## Elliptic curves in class 25200.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25200.q1 25200be6 [0, 0, 0, -2358075, -1393717750] [2] 393216
25200.q2 25200be4 [0, 0, 0, -153075, -20002750] [2, 2] 196608
25200.q3 25200be2 [0, 0, 0, -40575, 2834750] [2, 2] 98304
25200.q4 25200be1 [0, 0, 0, -39450, 3015875] [2] 49152 $$\Gamma_0(N)$$-optimal
25200.q5 25200be3 [0, 0, 0, 53925, 14080250] [2] 196608
25200.q6 25200be5 [0, 0, 0, 251925, -107887750] [2] 393216

## Rank

sage: E.rank()

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

## Modular form 25200.2.a.q

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 LMFDB numbering.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.